The Physics Teacher

mounted under the mass m2 was used for the sensor to take In order to estimate the experimental acceleration of m2, measurements properly due to the conical nature of the HC- the obtained data are curve fitted and the outcome is given SR04 sensor. by x = 32.8 cm/s/s t2 – 68.7 cm/s t + 38.1 cm. The data show a good agreement with the theoretical expression that is x= + Data collection details 6±5.(61/c2m) /ast22.. This effort gives an acceleration of m2 as x0 v0 t In order to collect the data, initially the HC-SR04 ultra- a= sonic distance sensor and Arduino Uno are connected to each The overall results for various mass couples obtained other in the following manner: VCC to 5V, GND to GND, experimentally and theoretically are given in Table I. The ECHO to 12, and TRIG to 13. After the connections, the rel- experimental results are extracted from the curve fits of the evant code (see appendix) is loaded into Arduino. Suppose experimental graphs. The theoretical acceleration values are that the direction of movement of mass m1 is downward upon basically calculated from Eq. (3) by substituting the corre- release. Then it is useful to push mass m1 slightly upwards ini- sponding values within the equation. tially; naturally after a short while, mass m1 stops, making the As can be seen in Table I, in repeated applications with dif- distance (d) take on its smallest value, and from this moment ferent masses, results consistent with theoretical calculations mass m1 moves downward and the system starts to move with have been obtained. In addition, the negative result shows that the obtained experimental results are also suitable for the vec- appropriate acceleration value.The mass m1 could also be released di- 40 rectly without pushing it up; how- ever, the data taken over Arduino Distance (cm) 35 x = 32.8 cm/s/s t2- 68.7 cm/s t +38.1 cm 30 are taken every 50 ms and the dis- tances are printed with an accuracy 25 of 0.01 cm; in this case, the position and time values of the system start 20 to be recorded with higher error 15 10 5 margins. Hence, the first value to 0 be selected is the smallest value of 0 0.5 1 1.5 2 d, and successive positions are se- lected as shown in the Fig. 3. Time (s) If the selected data are copied Fig. 4. The distance vs. time for the m1 = 61 g and m2 = 101 g mass Fig. 3. Original data ob- directly to Excel, they are taken into couples. tained from Arduino a single column so some data con- IDE. version must be performed (such as tor nature of the acceleration, and therefore the vector struc- ture of the acceleration can be emphasized with such a study. deleting the hours and minutes and extraneous symbols). Conclusion Once the data are in an appropriate two-column format in This study offers an alternative approach to teach import- Excel a scatter plot is drawn. A trend line is added to the chart ant topics such as kinematics, dynamics, and coding as a part and right-clicking on the line will go to the formatting menu. of STEM education. The theoretical dynamics and kinematics Here, x = At2 + Bt + C, polynomial option is selected, and the equations can practically be validated experimentally for equation is asked to be shown on the graph. teaching purposes. More specifically, the students can ana- lyze the position-time graphs of linear motion as a part of a Results pulley-mass system by performing the experiment, and also The pulley-mass systems are run a number of times for mathematical operations hence can calculate the acceleration of a complex system using dynamics laws. This study is bene- various mass couples and the distance of the m2 measured as a ficial for educational purposes because of its low cost and ease function of time. The first measurement that is performed for of establishment. the m1 = 61 g and m2 = 101 g mass couples is shown in Fig. 4. References Table I. The overall results obtained both experimentally and 1. Mustafa Cevik and Cihad Senturk, “Multidimensional 21st cen- theoretically and the percentage deviations. tury skills scale: Validity and reliability study,” Cypriot J. Educ. a (m/s2) Percentage Sci. 14, 11–28 (March 2019). Deviation (%) 2. Jiangyue Gu and Brian R. Belland, “Preparing Students with m1 (g) m2 (g) Experimental Theoretical 6.70 21st Century Skills: Integrating Scientific Knowledge, Skills, 101 60 0.51 and Epistemic Beliefs in Middle School Science Curricula,” in 141 141 3.20 3.00 11.00 Emerging Technologies for STEAM Education (Springer, Cham, 61 101 11.10 2015), pp. 39-66. 60 141 1.95 1.96 3. Lotta C. Larson and Teresa Northern Miller, “21st century skills: Prepare students for the future,” Kappa Delta Pi Rec. 47, 0.66 0.59 121–123 (July 2012). -0.48 -0.54 290 THE PHYSICS TEACHER ◆ Vol. 60, April 2022

4. Janice S. Morrison, “Attributes of STEM education: The stu- Look What’s in dent, the school, the classroom,” TIES (Teaching Institute for Excellence in STEM) 20, 2–7 (Aug. 2006). The Physics Store! 5. Alessandro D’Ausilio, “Arduino: A low-cost multipurpose lab Fizz: Nothing is equipment,” Behav. Res. Methods 44, 305–313 (June 2012). as it seems 6. Rattanaporn Puantha, Wilaiwan Khammarew, Anusorn Ton- by Zvi Schreiber gon, and Parinya Saphet, “The speed of sound in air of pipe acoustic resonance via the Arduino with LabVIEW interface,” A YOUNG WOMAN’S QUEST TO UNRAVEL THE UNIVERSE Phys. Educ. 54, 015009 (Nov. 2018). The future. In response to environmental degradation, the Eco-community sect eschews science and technology, 7. Azizahwati Azizahwati, Hendar Sudrajat, Fahrun Hidayat, and returning to an austere agricultural life of nature-worship. Muhammad Ridho, “Designing prototype learning media for But one young member, Fizz, struggles to reconcile these circular motion uniform based on Arduino Uno microcontrol- doctrines with her own burning curiosity. Risking life and ler,” J. Phys. Conf. Ser. 1351, 012064 (Nov. 2019). social standing, Fizz embarks on a quest that brings her face-to-face with the often-eccentric giants of physics, 8. Frédéric Bouquet, Cyrıl Dauphin, Fabienne Bernard, and Ju- from Aristotle and Galileo to Einstein and Hawking. One lien Bobroff, “Low-cost experiments with everyday objects for encounter at a time, Fizz pieces together the intricate homework assignments,” Phys. Educ. 54, 025001 (Jan. 2019). workings of our universe, while struggling with the resulting intellectual, moral, and personal challenges. 9. Antonio A. Moya, “An Arduino experiment to study free fall at schools,” Phys. Educ. 53, 055020 (Aug. 2018). All proceeds will be used to support AAPT’s Student Fund, which primarily goes to the 10. Ishafit Ishafit, Toni Kus Indratno, and Yudi Setio Prabowo, Outstanding Student program! “Arduino and LabVIEW-based remote data acquisition system for magnetic field of coils experiments,” Phys. Educ. 55, 025003 (Dec. 2019). 11. Parinya Saphet, Anusorn Tong-on, and Meechai Thepnurat, “One dimensional two-body collisions experiment based on LabVIEW interface with Arduino,” J. Phys. Conf. Ser. 901 (Sept. 2017). 12. Francisco Vera, Rodrigo Rivera, and Manuel Ortíz, “A simple experiment to measure the inverse square law of light in day- light conditions,” Eur. J. Phys. 35, 015015 (Dec. 2013). 13. Haider Kadhim Hoomod and Sadeem Marouf M. Al-Chalabi, “Objects detection and angles effectiveness by ultrasonic sen- sors HC-SR04,” Int. J. Sci Res. 6, 6 (June 2017). 14. Arduino Software, https://www.arduino.cc/en/Main/Software. Appendix. Code uploaded to Arduino Members: $7.50 Non-Members: $9.50 wOrdwerwyo.auraspnotw.oartg/store THE PHYSICS TEACHER ◆ Vol. 60, April 2022 291

A Simple Moment of Inertia Measurement Peter F. Hinrichsen, John Abbott College, Sainte Anne de Bellevue, Quebec, Canada Modern MEMs gyros/accelerometers allow the angu- lar velocity of pendula to be precisely measured and pentdhuelaunmg,uIlpaθr.. acceleration to be calculated. For a com- pound = – mga sin , where a is the distance of the center of mass from the pivot, so the moment of inertia Ip oramicfvgcteaehdleceaarcsnaotImbipoep=ndo–θe.u.m(tnθe=gdramp//2θie.n).n(wθed=dhubel/un2y)mmtfhraeeobampsoeuunmrtidtneuhaglesutuphmrieevmifosotehrccnoaetrnsiazonbofedntshltieaemvl.aepTnrlhygaruedmnlea-r required to maintain the pendulum in a horizontal position. Introduction The concept of inertial mass, although sometimes confused Fig. 1. A Flying Dutchman hull suspended from a crossbar for wcFoointrhsrtowatneaittgioohfntp,airlsomgpeoonrtietoironanlNlayleiutwnytdionenr’Nsstseoewoctodonbnd’yslusaenwcdosentradgterlaasdwthuFaatt=esm=ar.s.I.tθ.h.,e measurement of its period of oscillation in order to determine its moment of inertia, before competing at the 1976 Olympics. i.e., the applied torque  θe..q. uAaltlshtohuegmh tohmiseanptpoefairnsesritmiaiIlatri,mthees the angular acceleration moment of inertia I of a body is conceptually more complex. It depends on the shape of the body, and on the location and orientation of the axis of rotation relative to the body, i.e., it is a tensor.1 For rotation about a fixed axis, only one diagonal el- ement of the moment of inertia tensor is required, i.e., a single scalar number. Another significant difference is that gravita- etiqouniavlamlenaststomin, ie.ret.,ia“lwmeaigssh,tiW.e.,/G“FroarvcietaFti/oanccael laecrcaetileornatr.i.o”nsog”thise mass can be determined by weighing rather than from New- tmonea’sssuerceodnadsla“wTo. Trqhueemo/ mAnengtuolafrinacecretilae,rhatoiownevθ.e.”r., can only be Some of the sailboats at the Olympic Games have a rule that (b) the moment of inertia of the hull must be above a specified Fig. 2. (a) A compound pendulum of mass m, moment of inertia value, as it affects their performance in waves. Thus, before Ip about the pivot, and center of mass at a distance a from the pivot, deflected by an angle from the tvheertiacnagl.uAlarMvEeMloScigtyyro./. the Games begin, the moments of inertia of the hulls were all accelerometer at the pivot measures measured by suspending them as compound pendulums.2 The The accelerometer can be used to measure the angle . (b) A technique relies on measurements of the small angle period of photograph of the pendulum, with the inset showing the MEMS oscillation3 . It requires two measure- gyro/accelerometer at the axis. ments at center of mass heights a1 and a2 = a1 + b, the measure- approximation sin . MEMS gyros/accelerometers, such ments being a known distance b apart, in order to determine as those in smartphones, provide direct measurements of the taohlfseionrbeardeteiiunasIuo=sfemgdykor2natafibouonllukstizathendedcateihrnectnrea,rfaotf4ft-e6mrawansedsi.goThnhinmisgot,edtchehernnmidqourmoenehenasts.7 angular velocities of rotating bodies.14 Alternatively, if the ra- dial position of the sensor is known, the angular acceleration can be derived from the tangential and radial accelerations as My experience of explaining the effect of the moment of inertia measured by the accelerometer. However, due to the nature of on the speed of their sailboats in waves to sailors at the Olym- the othuetpauntgouflatrheacaccecleelreartoiomneθt.e. r=s,dth./idstisdmireocrtelycoams tphleex“r.aDteeroifv- pic Games, many of whom were engineers, is that a practical ing demonstration was worth a thousand words. I believe that this change of the measured angular velocity” is both simple and also applies to most physics students. clearer pedagogically. The moment of inertia Ip of a pendu- The literature contains a number of papers on undergrad- lum about tohfethpeivaontgcualnarbaecdcierleecrtaltyiodnetθ.e.ramnidntehdeftroormqume ea-that uate measurements of moments of inertia8-13 that require surements precise timing measurements and are based on a solution of produces it. For example, a simple pendulum when swinging the pendulum equation. The object of this paper is to describe td–Ihausrθlp.ou(.θθum.=.g=hi/s2–9I)0Isasponp=cdgo/mtrahr,aees2sot.poItonrhnqecudomesmtaoopbmaofrreueintsetotfhonaeflalipnociefovrtomhttiepaisomoufantshd/s2e,p=sseoi–mngmdp=uglelaup=men- a simple measurement of the moment of inertia of a p/θe..n. Tduhliusm, which is a direct application of the definition I = does not require a solution of the pendulum equation or the 292 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0009995

Ip .. = –mga sin . (1) θ Fo.r. small angles this equation can be approximated as Ipθ –mga , which has the oscillatory solution (t) = 0 cos ( t + ), with 2 = mga/Ip = 4 2/T0­2, where T0 is the period of small amplitude oscillation. The phase depends on the initial conditions.3 The classical compound pendulum method of determining moments of inertia2 is to measure the period of oscillation, and then Ip = mgaT0­2 / 4 2. (2) (c) However, for the present experiment the exact Eq. (1) is employed at an angular deflection of = 90o [see Fig. 3(a)], lia.er.,awccheelnertahtieopneθn..(dtu) ltuhmenishhasoirtiszomnatxailmanudmsivnalu=e,1s.oT: he angu- Fig. 3. (a) A compound pendulum at 90o, after Ip = –mga/θ.(.θ= /2) = –mga/θ..max. (3) release at > 90o from the vertical. A MEMS gyro/ accelerometer at the pivot measures the angular Alternatively it is instructive to present this by taking mo- velocity and the angle. (b) and (c) The measure- ments about the center of mass of the horizontal pendulum: ment of the force, applied at a distance l from the pivot, in order to support the pendulum horizon- Rza = –Icm .. /2, (4) tally. θ θ= at 90o requires a torque to rotate it about its center of mass, where Rz is the vertical component of the pivot reaction [see which is provided by the vertical component of the pivot re- Fig. 3(a)] and Icm is the pendulum moment of inertia about action. Thus the center of mass is no longer in free fall and the the center of mass. The net vertical force on the horizontal athnagtuIlpar=a–cmceglaer/aθ.(t.θio=n/i2s) less than g/a. However, it is still true zp..e=nR adzθu.–.θlum=mg/2=issmRo:zz..–=magθ.,.θw=hi/c2h. produces the vertical acceleration , which can then be used to measure Ip. (5) Theory The weight force mg of a pendulum of mass m acting at a Substituting Eq. (4), distance a from the pivot exerts a torque  = –mga sin about , the pivot when the pendulum is displaced by an angle from (6) tahcecevleerrtaitciaoln(sθ.e.(et)F=ig. 2(t))./TIph,iws thoerrqeuIep then produces an angular (7) is the moment of inertia and applying Steiner’s theorem, Ip = Icm + ma2 : of the pendulum about the horizontal axis. In the absence of damping, this then leads to the pendulum equation3: Fig. 4. The angular velocity (diamonds), the averaged angular Fig. 5. The angular accelerations vs. the sine of the angular acceleration as derived by numerical differentiation (circles), and displacement for amplitudes 1.57 rad (red triangles), 1.97 rad -10 times angular displacement, as derived by numerical integra¬- (blue circles), and 2.79 rad (green diamonds). The slope is tion (open triangles). Data for amplitude 1.57 rad (90o) red, 1.97 rad (103o) blue, and 2.79 rad (160o) green points. The times are shifted –msgl/Ip = –24.935 0.005 s–2. so as to align the maxima in the angular acceleration. The dashed lines indicate the maximum slopes of the angular velocities. THE PHYSICS TEACHER ◆ Vol. 60, April 2022 293

In the absence of damping, conservation of energy leads to a a , (10) where 0 is the angle of release, i.e., the amplitude. Then (11) So a plot of .2 vs. cos is linear with a slope of 2mga/Ip, i.e., (12) Fig. 6. The square of the angular velocity vs. the cosine of the Any real system is subject to drag torques, which have not angular displacement, for amplitudes 1.57 rad (red triangles), 1.97 been included in Eq. (1). For release from rest at angles only rad (blue circles), and 2.79 rad (green diamonds). slightly greater than 90o, the velocity at 90o will be minimal and thus the effects of viscous or turbulent air drag will be Table I. Results. negligible. This leaves frictional torque at the bearing. The vheorrtiizcoanl traela,catsiodnetfeorrmceinRezdatbtyhteakpiinvogtm16owmheenntsthaebpouent dthuelucmeni-s Analysis Moment of Inertia Ip 10–2 kg.m fthR1oe.ox5rrr=7oaizfrmboamendaaatrta.sh2ilsn(e,θ(gsi=aseoneR/fg2Fzru)ai=algdan.mrid4uvg)spe(ib1lisovw–socmitimttfyahralilc2c.,(/otθsIi=eopof)nft./ih2Fc)eioeRwhrnxoahtrmieosinzfpvofetlrnihrittcyueatdspliomepensniavcdlolluo,.ttlTsruheehmeateocrniats,itoion of the frictional to the gravitational torque is msgl 0.304 ± 0.001 Nm f /mga = b(1 – ma2/Ip)/a. Thus this correction is propor- Amplitude 1.57 rad 1.97 rad 2.79 rad tional to b/a, which is typically small. It also depends on Ip , and is zero for a simple pendulum. 1.28 ± 0.01 1.33 ± 0.01 1.32 ± 0.01 1.25 ± 0.01 1.26 ± 0.01 1.27 ± 0.01 1.28 ± 0.01 1.26 ± 0.01 1.27 ± 0.01 1.26 ± 0.004 Results The test body (see Fig. 2) consisted of a 1-in diameter steel Calculated 1.28 ± 0.02 ball bearing glued to a coat hanger wire, which was wound The gravitational torque mga can be determined from the round a plastic housing for two ¼-in ID ball bearings mount- mforacinetmaisngtahpepplieenddautlaumdishtoanriczeolnftraolm[seteheFipgi.v3o(tbi)n].oTrdheernto ed on a stainless steel shaft. The pendulum had a total mass mkngoaw=nm. Asgltlesrontahtievmelyastshoefmthaesspmencdaunlubme mdoeaessunroetdnaeneddtthoebe 97.9 ± 0.1 g and length 416 ± 2 mm to the center of the ball. balance point used to determine a. The balance point of the pendulum was at 316 ± 1 mm from Then Ip = –msgl/ θ..max. the axis. The moment of inertia of the pendulum about the ax- (8) is, based on an estimate of the contribution of the bearing, was cMalEcMulSatIeMd tUosbaeccIpel=er1o.m28e3te1r0/g–y2rkog1.7mo2f.rAesloigluhttio(4ng0).0B5ludeetgo/osth l(mAadtrat.vx/heidemlto)iuncmimtatryxo.swdNlouaopvcteteeofootrfhyrtamhlteefviosaernlm,sgθw.ou.mrilenaarxgtrvcaieaamlnnopgcbulieittlyaudrdvettsehe.srtanimnmeisaenirned9dua0stfoaortoiθhd.m.mealaat,x1nh5eg=suo- was mounted on the rotation axis of the pendulum (see Fig. 2) the slope can easily be determined (see Fig. 4). and recorded data at a sampling rate of 200 Hz. At the intermediate level the ianntgeugrlaartevdeltooccitaylcdualtaatecaθ.n.(tb)aend numerically differentiated, and acceleration The scale reading when the pendulum was supported at θ.(.(tt)). Then a plot of Eq. (1), i.e., the angular a slope 350 1 mm from the axis [see Fig. 3(b)] was 88.95 0.05 gm, as a function of sin (t), is linear with tmhaus=m0s.0l 3=009.0301.100002.0k0g0·m1 kdge·rmiv,ewdhfircohmagthreeemd awsisthand –mga/Ip = –msgl/Ip, so: balance point. (9) For the student experiment the pendulum should be re- leased at an angular displacement somewhat larger than 90o, the exact value being unimportant, and the pendulum needs only to swing through one oscillation. In order to avoid initial transients, the data from the second half oscillation should be analyzed. However, the data presented in Figs. 4-6 have been extracted from a long recording of the decaying angular veloc- ity of the pendulum after release at ~180o. These data (see Fig. 4) then demonstrate that the maximum angular acceleration 294 THE PHYSICS TEACHER ◆ Vol. 60, April 2022

is independent of the amplitudes (above 90o). The moments of of the moment of inertia Ip. For comparison the moment of inertia derived from the maximum angular accelerations, as inertia can also be derived from the period T0 of small angle determined from the slopes of the raw angular velocity data, oscillation. It is interesting to note that this method is essen- are listed in Table I. tially similar to that proposed by Watt Webb for “in the water” For intermediate students the analysis can be extended by measurements of the moments of inertia of large keelboats.18 numerically integrating and differentiating the angular veloc- ity data. The integration requires the value of the initial angu- References lar displacement. For the present data this was known to be 1. R. Douglas Gregory, Classical Mechanics, 1st ed. (Cambridge 180o, but otherwise can be simply determined from the initial stationary accelerometer data. The derived angular accelera- University Press, Cambridge, 2006). tion, which was somewhat noisy, was averaged over 2. Peter F. Hinrichsen, “Practical applications of the compound 0.5 s and is seen to have a broad maximum, as shown in Fig. 4m. eTnotsd,etmheoannstgrualtaertahcacteEleqr.a(t1io)napθ.p. wlieass at all angular displace- pendulum,” Phys. Teach. 19, 286–292 (May 1981). plotted vs. sin (see Fig. 3. Stephen T. Thornton and Jerry B. Marion, Classical Dynamics 5). The tshloepaem–pmlistguld/Iep, of this graph, which is again indepen- dent of was then used to calculate the moment of Particles and Systems (Thompson Brooks Cole, Belmont, CA, of inertia (see Table I). 2004). In order to demonstrate that energy is conserved (almost), 4. M. W. Green, “Measurement of the Moments of Inertia of Full the square of the angular velocity was plotted vs. cos (see Scale Aircraft,” in Technical Notes National Advisory Committee Fig. 6). The moment of inertia was then calculated from the for Aeronautics (Langley Memorial Aeronautical Laboratory, slopes 2mga/Ip of these graphs and is shown in Table I. The Washington, DC, 1927), pp. 1–18. slope is again independent of the amplitude (see Fig. 6). The 5. William Gracey, “The Experimental Determination of the Mo- cos intercept was used to confirm the amplitude. ments of Inertia of Airplanes by a Simplified Compound-Pen- For comparison with the classical method of pendulum dulum Method,” in Technical Note National Advisory Committee moment of inertia measurement, the period of small ampli- for Aeronautics (1629) (1948), p. 26. tude oscillations was measured as 1.279 ± 0.001 s and led to 6. David Wolfe and Chris Regan, “Frequency Shift During Mass Ip = 1.26 ± 0.004 3 10–2 kg·m. Properties Testing Using Compound Pendulum Method,” Dryden Flight Research Center (NASA/TM–2012-216017). Conclusions 7. Amir Teimourian and Dariush Firouzbakht, “A Practical Meth- od for Determination of the Moments of Inertia of Unmanned A simple method for measuring the moment of inertia Aerial Vehicles,” in Italian Association of Aeronautics and Astro- ab=ouIθt. .ahhaos rbiezeonntdael sacxriisbtehda.tTdhireeecxtlpyearpimpleinest Newton’s law nautics XXI Conference (Napoli, 2013). exploits the sim- 8. Dale L. Schruben, “Novel method of measuring inertial mo- plification of the theory of pendulum motion when it swings ment,” Am. J. Phys. 36, 460–461 (May 1968). tothhnerotmhuegehahsoturhriezeodhnoatrnaigzl uopnleantradvl.ueAlluosmctiatiytsicθc.omomfeatbhsiunerepedemnwedintuhtluothmf ethasesloitptoserwqθ.ui.noegfs 9. H. L. Armstrong, “An experiment on the inertial properties of a through 90o. This directly determines the moment of inertia rigid body,” Phys. Educ. 20 (3), 138–141 (1985). Ip of the pendulum about its pivot. Despite the large angular 10. W. N. Mei and Dan Wilkins, “Making a pitch for the center displacements involved, the analysis does not require the of mass and the moment of inertia,” Am. J. Phys. 65, 903–907 solution of the nonlinear pendulum equation, or the approxi- (Sept. 1997). mation sin . In fact for the introductory version only Eqs. 11. Stephen Van Hook, Adam Lark, Jeff Hodges, Eric Celebrezze, (5)-(7) are required. and Lindsey Channels, “Playground physics: Determining the moment of inertia of a merry-go-round,” Phys. Teach. 45, 85–87 The torque measurement does not require any precise (Feb. 2007). alignment as the pendulum only has to be within ±3o of hor- 12. Carlos Alberto Fonzar Pintão, Moacir P. de Souza Filho, Wesley izontal. If the pendulum is released close to 90o , then the Fernando Usida, and José A. Xavier, “Experimental study of angular acceleration has a broad maximum (see Fig. 4), so the the moment of inertia of a cone,” Eur. J. Phys. 28 (2), 191–200 angular velocity plot vs. time is ocflothseetsololipneeθa..r. in the region (2007). 90o, facilitating calculation Extensive data, 13. Matthaios Patrinopoulos and Chrysovalantis Kefalis, “Angular have been presented in order velocity direct measurement and moment of inertia calculation recorded with a MEMS gyro,17 of a rigid body using a smartphone,” Phys. Teach. 53, 564–565 to justify this simple experiment. The student experiment can, (Dec. 2015). however, be performed with a smartphone and only requires 14. A. Kaps and F. Stallmach, “Tilting motion and the moment of the gyro angular velocity data for a single oscillation of am- inertia of the smartphone,” Phys. Teach. 58, 216–217 (March plitude greater than 90o. The more advanced students can nu- 2020). pamnloedrtipclao.2ltlyvθ.s.in.vcsteo. gssirnatteotaoinnvdveedrsiitffiyfgetarhteeencptoieanntesdeturhlveuamatinoegnquoulafarteivnoeenlro,gacyin.tdyT/hdoearta 15. Peter F. Hinrichsen, “Fourier analysis of the non-linear pendu- slopes of these linear graphs then provide a more precise value lum,” Am. J. Phys. 88, 1068–1075 (Dec. 2020). 16. Peter F. Hinrichsen, “Compound Pendulum pivot force,” Eur. J. Phys. 42, 025001 (2020). 17. MbientLab Inc., “Metamotion MMR Wearable Bluetooth 9-axis IMU” (2018), https://mbientlab.com/. 18. Richard S. McCurdy, presented at the New England Sailing Yacht Symposium, March 23, 1990, U.S. Coast Guard Academy, New London, CT, 1990. THE PHYSICS TEACHER ◆ Vol. 60, April 2022 295

Investigating Students’ Experience of Instructional Videos with the UX Curve Method Guangtian Zhu and Yi Ding, Faculty of Education, East China Normal University, Shanghai, China Qingwei Chen, ShenZhen Foreign Languages School (Group), Shenzhen, China IYuhan Huang, Chengdu Jiaxiang Foreign Languages School, Chengdu, Chinathe Nokia research center to assist customers in reporting how nstructional videos are commonly used in both remote and why their experiences with mobile phones had changed and in-campus curriculum. In order to investigate over time.8 Besides consumer products such as mobile phones students’ experience when learning with online in- or pruning shears, the UX curve method was also applied in structional videos, we adapted a method called “UX curve” from the user experience studies in industrial design. In studying users’ experience with virtual services such as video this paper, we introduce the procedure and data processing games.8-10 The practice of using UX curves is similar to the method of using the UX curve method. We applied the UX observational tools such as COPUS (The Classroom Observa- curve method in a high school physics class while the stu- tion Protocol for Undergraduate STEM) or RTOP (Reformed dents were watching an instructional video of kinematics. Teaching Observation Protocol), which require researchers or The results suggested that the UX curve method is practical, co-instructors to describe the instructor’s teaching process in convenient, and effective in collecting students’ real-time real time.11-12 The main difference is that the UX curve meth- experience. od as described here is for students to describe their direct experience rather than the third-party observers. Background of the UX curve method Applying the UX curve method in class Instructional video plays an important role in different We use the UX curve method to collect 35 10th-graders’ types of online teaching activities. In MOOCs (Massive Open Online Courses) and SPOCs (Small Private Online instant feelings when they are watching an instructional video Courses), instructional video is the major resource for stu- of relative movement (e.g., the relative velocity of ship A as dents to learn new content. For real-time online teaching observed by a sailor on ship B). The 19-minute-long video is via Skype or Zoom, the recorded instructional videos can presented in the format of “powerpoint (PPT) + handwrit- also be used as revision materials or make-up courses. Re- ing.” The instructor in the video uses a PPT and handwriting searchers have created surveys and questionnaires to probe tablet to present content, while his own image is not shown students’ overall attitudes and experiences after they had on screen. The video does not contain embedded interaction learned with some online instructional videos.1-2 Survey points such as clicker questions. Such format is commonly results suggest that poor experience with instructional vid- used by physics teachers when they create instructional videos eos can cause higher dropout rate for online learners.1 The by themselves. assessment of students’ learning experience of online video lectures may assist in improving the quality of future online The 35 students involved in our study are a whole class in courses.2 school and physics is a required course for them. These stu- dents have three to four 45-minute physics classes every week. Current surveys of students’ online learning experience They usually use the instructional videos as self-learning ma- are usually conducted after an online lesson or at the end terials when reviewing the sessions that they have difficulties of a whole online curriculum.3-4 As we know, students’ ex- with. In order to avoid students’ distraction and effectively perience with an instructional video may fluctuate during collect UX curve data in our study, all students are required to the video stream. For example, at the beginning students watch a video in recitation class after their school teacher has may be interested in a sample question with funny cartoon taught the corresponding content in regular class. elements, but then they start to feel bored after a five-min- Before students watched the videos, the teachers intro- ute instruction on this question with a monotonous voice. However, students’ fluctuating experiences may not be duced the necessary steps of the data recording process fully recalled after they have finished watching the video. and provided a template with instructions to the students. Psychological studies have also suggested that people can- Students needed to draw a two-dimensional graph with hori- not recall all the details of their past experiences, and their zontal axis as time and vertical axis as positive/negative expe- memory often introduces systematic biases into evalua- riences. When the instructional video was being played, stu- tions.5-7 Hence some features of students’ learning experi- dents needed to use brief keywords to mark down the instant that they noticed something remarkable about the video. Af- ences through online videos may be missing in the post hoc ter the video stream ended, the students connected the points surveys. into UX curves (we called them “experience-time graphs” in the template provided to the students). The original template The UX curve method originates from the user expe- was written in Chinese and the translated version is shown rience studies in industrial design.8-9 Users of a product below in italics. need to sketch a curve on a paper with written comments Thank you for participating in the study of experi- to report how their experience changes. This method was originally proposed by user experience researchers from 296 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0009996

ence with online instructional videos. The length of the video is about 20 minutes and a timer is shown on the upper right corner of the video. Please record your experience in five levels of “2/very good, 1/ good, 0/neutral, -1/bad, -2/very bad.” You need to complete the following steps: Step 1. Prepare an A4 size paper and draw a coordinate as Fig. 1. The coordinate template provided to each student in shown in Fig 1. The horizontal axis represents time and the user experience study. The horizontal axis represents time the vertical axis represents the level of your experience. and the vertical axis represents positive/negative experiences. Students need to draw this coordinate on an A4 size paper before Step 2. While watching the video, please mark down a point recording their experience. on the experience-time coordinate at the instant when you have a remarkable experience. Nearby each point you draw, write brief keywords about why you have the posi- tive/negative experience. Step 3. After the video stream has ended, connect the points on your coordinate to form an experience-time graph. A sample experience-time graph is shown in Fig. 2. You can also further explain your remarkable experiences if you feel they are not clearly stated in Step 2. Data processing Fig. 2. A sample experience-time graph. Students’ short descrip- Students’ real-time experiences of the instructional videos tions next to each point indicated the reasons that caused their remarkable experiences. are very diverse due to their individual differences. But if a particular feature in a video causes a common remarkable Fig. 3. The distribution of the noteworthy experiences of one experience among a portion of students, such feature must be video marked by 35 students. Different levels of experiences are worth noting. In order to find out the common features of in- marked by different colors. The horizontal axis is the sequence structional videos that induce remarkable experiences, we di- of time intervals (20 seconds in one interval). The vertical axis is vided the whole time span of a video stream into small pieces a percentage of remarkable experiences in one interval (number (e.g., 20 seconds) and counted the total number of experiences of experiences reported at the time interval/total number of stu- reported within each time interval. The time intervals were dents). The percentages of negative experiences are denoted by labeled in consecutive sequence. The data on the boundary negative values. between two consecutive time intervals were counted only in the earlier one. If more than 20% of the students have either positive or negative feeling in one interval, we will further analyze the corresponding explanations of the remarkable experiences. The 35 students involved in our study provided effective UX curves with altogether 194 reasons of noteworthy expe- riences. On average, each student provided 5.5 ± 1.6 pieces of remarkable experiences. The median of the number of remarkable experiences provided by each student is 5. The distribution of the noteworthy experiences of the first video reported by 35 students is shown in Fig. 3. The horizontal axis is the sequence of time intervals and the vertical axis is the percentage of remarkable experiences reported in the time in- terval. Different levels of experiences are marked by different colors. For example, in the first time interval (0:00-0:20), three students’ experiences were very bad, 12 students’ experiences were bad, and two students’ experiences were good. Hence from bottom to top, the length of the left-most bar on the graph is 8.6% blue (i.e., 3 out of 35), 34.3% orange, and 5.7% yellow. Note that we present the negative experiences by neg- ative percentage values in order to better differentiate positive and negative experiences. THE PHYSICS TEACHER ◆ Vol. 60, April 2022 297

Students’ experiences reflected in the UX interview with the students based on these keywords can curves provide more details about the crucial factors that affected students’ learning experience. (3) In order to match the time- Students’ experiences were affected by the auditory and line for all students in class, remember to show the timer on visual factors of an instructional video. For example, all the screen or bring a digital clock with minute-second format to experience values in time interval 2 [0:20-0:40] were negative the classroom. and five students expressed a feeling of being dazed/dizziness due to a huge yellow cursor on the screen. In time interval 7 References [2:00-2:20], three students had a positive experience because 1. Yan Wu, “Factors impacting students’ online learning experi- of the clear and logical blackboard writing. However, at the same time, six students held a negative experience when the ence in a learner‐centred course,” J. Comput. Assisted Learn. 32, teacher kept repeating his pet phrase “according to common 416–429 (May 2016). sense” (in Chinese) over and over again. 2. Tal Soffer, Tali Kahan, and Eynat Livne,“E-assessment of online academic courses via students' activities and perceptions,” Stud. In addition, students may have negative feelings if the Educ. Eval. 54, 83–93 (Sept. 2017). length of time left by the teacher to consider a question was 3. Pilar Gómez-Rey, Elena Barbera, and Francisco Fernández-Na- limited. In time interval 3 [0:40-1:00], eight students asserted varro, “Measuring teachers and learners’ perceptions of the that the time given by the teacher was too short (only nine quality of their online learning experience,” Distance Educ. 37, seconds) to solve a problem. In the following time interval 4 146–163 (March 2016). [1:00-1:20], six students thought that the connection between 4. Dominique Monolescu and Catherine Schifter, “Online focus two questions was improper because the teacher continued to group: A tool to evaluate online students’ course experience,” explain the second question without giving any explanation Internet High. Educ. 2, 171–176 (Spring 1999). to the previous one. A similar phenomenon also occurred in 5. Derek A. Muller, Manjula D. Sharma, and Peter Reimann, time interval 30 [9:40-10:00]. More than half of the students “Raising cognitive load with linear multimedia to promote con- marked a negative experience when the instructor asked ceptual change,” Sci. Educ. 92, 278–296 (Jan. 2008). them to answer a multiple-choice question in only three sec- 6. Christopher K. Hsee and Reid Hastie, “Decision and experi- onds. ence: Why don't we choose what makes us happy?” Trends Cog- nit. Sci. 10, 31–37 (Jan. 2006). Conclusion 7. Donald A. Norman, “THE WAY I SEE ITMemory is more im- Students’ learning experience is as important as their portant than actuality,” Interactions 16, 24–26 (2009). 8. S. Kujala, V. Roto, K. Väänänen-Vainio-Mattila, E. Karapanos, learning outcomes. Some students may argue that they have and A. Sinnelä, “UX curve: A method for evaluating long-term acquired academic achievement in a course they do not like. user experience,” Interact. Comput. 23, 473–483 (Sept. 2011). However, increasing evidence suggests that learners lacking 9. J. Varsaluoma and F. Sahar, in Measuring Retrospective User good emotional experience in their academic life can easily Experience of Non-Powered Hand Tools: An Exploratory Remote disengage in their learning process both behaviorally and Study with UX Curve, 18th Int. (ACM Press, Tampere, Finland, cognitively.13-14 Therefore, teachers should pay great atten- 2014), pp. 40–47. tion to their students’ experience in the learning process. 10. J. Vissers, L. De Bot, and B. Zaman, in MemoLine: Evaluating Long-Term UX with Children, 12th Int. (ACM Press, New York, The UX curve is a convenient tool to collect students’ 2013), pp. 285–288. real-time experience of instructional videos. Actually, it can 11. Patrice Marie Ludwig and Samantha Colleen Bates Prins, “A be applied for evaluating in-person teaching as well. The UX validated novel tool for capturing faculty-student joint behav- curve method is useful for teachers as an instructor to learn iors with the COPUS instrument,” J. Microbiol. Biol. Educ. 20, about important positive and negative features in their teach- 40 (Dec. 2019). ing, as perceived by their particular group of students. There- 12. Charles Doug Czajka and David McConnell, “The adoption fore, teachers can do more of the things their students find of student-centered teaching materials as a professional de- positive, and less of those they find negative, so as to improve velopment experience for college faculty,” Int. J. Sci. Educ. 41, the teaching quality and students' positive attitude towards 693–711 (Feb. 2019). the course. 13. Jennifer A. Fredricks, Michael Filsecker, and Michael A. Law- son, “Student engagement, context, and adjustment: Addressing For teachers interested in applying the UX curve meth- definitional, measurement, and methodological issues,” Learn. od in their classes, here are some tips that might be useful: Instr. 43, 1–4 (June 2016). (1) The UX curve method can be applied at any time of the 14. I. Archambault, M. Janosz, J. S. Fallu, and L. S. Pagani, “Student semester, but it should not be applied too frequently since engagement and its relationship with early high school drop- students’ attention to the course content may be more or less out,” J. Adolescence 32, 651–670 (June 2009). distracted when recording their experiences. Monthly or biweekly application of the UX curve method is suitable for teachers to probe their students’ real-time learning experi- ence. (2) While analyzing the UX curve data, teachers can focus on the keywords of the moments that many students (e.g., more than 20%) considered as noteworthy. A follow-up 298 THE PHYSICS TEACHER ◆ Vol. 60, April 2022

Millikan Again one quarter the diameter of a human red blood cell) latex sphere of weight mg in the uniform electric field between two William M. Wehrbein, Nebraska Wesleyan University, Lincoln, NE parallel plates a distance d apart (Fig. 1). Recognized as one of the most beautiful experiments Prior to Event 1 the electrical potential between the plates of all time,1 the oil drop experiment2 performed by is adjusted to a value called (unfortunately) the “set charge” Robert Millikan3 and his graduate students (primarily at which the sphere hovers in a roughly stationary position. Harvey Fletcher4) is a standard in the repertoire of experi- (This value will be referred to as V in this paper.) The motion ments performed by undergraduate physics students. How- of the sphere is then controlled by a switch with four settings: ever, “as a teaching lab it does not enjoy a good reputation “extra charge,” “set charge,” “0,” and an unlabelled setting that for three reasons: eyestrain, tedium, and poor, unconvincing is the same magnitude as, but opposite polarization of, “set results.”5,6 Several have attempted to make this experiment charge.” The setting “extra charge” is an unknown potential more student-friendly by improving the optics and replacing greater than “set charge” used to reposition the sphere in the the stopwatch with a computer,5 replacing the eye with a video field of view. camera,7,8 and utilizing video analysis tools.9 Currently avail- able versions of the oil drop apparatus for high school and col- Each of the 12 events consists of one to six “episodes” lege students have incorporated a number of these features.10 (which I have designated as a, b, c,…) based on the setting of On the other hand, others are ready to replace the experiment the switch and the charge of the sphere, where the motion of with interactive computer-based simulations.11,12 There is the sphere is nearly uniform. Between some events the space another alternative: Have students analyze pre-recorded vid- around the sphere is bathed in x-rays. Because the potential eos of the Millikan experiment. Besides the “Millikan Mov- is unknown when the switch is set on “extra,” these episodes ies”13 produced at the California State University at Chico, the aren’t useful in determining the charge of the electron. In collection “Physics: CINEMA CLASSICS”14 (“PCC”) contains addition, some episodes have been deemed too short or not the essential nuggets from a Physical Science Study Commit- straight enough to be included in this analysis. tee (PSSC) educational film made in 1959 sufficient to com- pute the elementary electric charge. Theory The “PCC” video clips There are three forces acting on the sphere: an electric For a number of years at my college we have used the Mil- force Fe with magnitude nqeE, where E = V/d is the magni- tude of the electric field, n is the number of extra elementary likan Experiment chapter on the original “PCC” LaserDisc as charges on the sphere, and qe is the magnitude of the charge an individual experiment in our junior-level advanced labora- of the electron; the gravitational force Fg with magnitude mg; tory course. Students taped a clear plastic sheet to the monitor and drag force Fd with magnitude kv, where k is the drag coef- screen to calibrate the reticle and used the frame counter on 1fi0c-i4enmt/asn(drovuigshthlyeaspfoeoetdp. Terhheotyupr)ic—alrsepsueletds of a sphere—about the disc player as a stopwatch. The process was awkward, in a Reynolds but the results were acceptable. LaserDisc technology all but number less than 10-5, indicating that a model with linear disappeared two decades ago. But “PCC” is available again as drag (i.e., Stokes’ law) is appropriate. a set of DVDs.15 Most of the tedious elements of experiment can be done easily today using modern physics education There are three cases: software, and the data on video clips can be analyzed in finer If the sphere rises (illustrated in Fig. 2), then the electric force detail to reveal some surprises. must balance the gravitational force plus the drag force, so Beginning with a detailed tour of a real Millikan apparatus outfitted with a motion picture camera, there are 12 video clips (called “Events”) of the motion of a microscopic (about Fig. 1. One frame of the “PCC” video clip. Latex sphere Fig. 2. Free-body diagram for sphere with mass located at bottom center; scale in arbitrary units. m and charge nqe in Event 5 (n = 3). DOI: 10.1119/5.0026266 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 299

Table I. Data derived from Millikan Experiment chapter of “Physics: CINEMA CLASSICS.” Units for nqe E + mg = kv. (1c) entries in columns six through eight are pixels/frame. Event episode slope uncert v0 v± assigned v±/v0 1+ v±/v0 assigned If we define v± as the signed v0 n vertical velocity, with up- -33.31 0.1292 ward positive, then the 1 d zero -34.8 0.0576 33.31 -2.1 -1.1 -2 same equation can describe 2 d zero -68.01 0.08062 34.8 0.017 1.017 2 the first two cases. Fur- 3 d –set 0.5503 0.05625 -2.1 -1.1 -2 thermore, if we replace the 4 b set -67.79 0.07501 -68 32 0.53 1.53 3 unassigned n with –n in the 4 c –set 16.62 0.02243 0.55 32 third case, then all cases can 5 set -68 32 be described with the single 17 32 equation 6 a set 15.73 0.06441 16 32 0.5 1.50 3 nqe E = mg + kv±. (2) 0.94 1.94 4 When the electrical force 6 b set 29.62 0.6235 30 32 on the sphere is zero, either 0.97 1.97 4 because E = 0 or n = 0, then 6 c zero -33.11 0.03096 33.11 1.5 2.5 5 the drag force balances the gravitational force and 6 d set 30.99 0.09787 31 32 1.9 2.9 6 the sphere falls downward with a characteristic termi- 7 a set 48.52 0.1246 49 32 1.9 2.9 6 nal speed v0, so kv0 = mg, indicating that k = mg/v0. 7 b zero -30.37 0.08831 30.37 1.6 2.6 6 Therefore the force balance in every case is described by 7 c set 61.08 0.3756 61 32 7 d zero -29.1 0.02771 29.1 7 e set 62.23 0.06316 62 32 7 f zero -32.16 0.4858 32.16 8 a set 50.94 0.4864 51 32 8 b zero -28.61 0.05021 28.61 (3) 8 c set 53.26 0.1661 53 32 1.7 2.7 6 8 d zero -29.33 0.03142 29.33 8 e set 47.64 0.07602 48 32 1.5 2.5 5 Procedure 8 f zero -28.61 0.2789 28.61 First, the video clips must be converted from 9 a set 47.33 0.2563 47 32 1.5 2.5 5 9 b set 35.16 0.1601 35 32 1.1 2.1 4 DVD to a video format that 9 c set 15.12 0.09888 15 32 0.47 1.47 3 can be read by an appropri- ate video analysis tool. We 9 d zero -33.03 0.03351 33.03 used Handbrake,16 a free open source video transcod- 9 e set 17.93 0.06961 18 32 0.56 1.56 3 10 a zero -32.57 0.1572 32.57 er, to convert the clips, and 10 b set 16.35 0.175 16 32 0.5 1.50 3 carried out video analysis using Tracker17 from the 10 c set 34.64 0.1774 35 32 1.1 2.1 4 Open Source Physics Proj- ect.18 10 d set 13.61 0.1046 14 32 0.44 1.44 3 10 e zero -34.15 0.06855 34.15 Tracker was used in “au- totracker” mode to record 10 f set 15.22 0.07001 15 32 0.47 1.47 3 11 set -16.99 0.1776 -17 32 -0.53 0.47 1 the position of the sphere 12 a set -16.96 0.2311 -17 32 -0.53 0.47 1 in each frame. We shall see that the analysis depends 12 c (zero) -31.52 0.02009 31.52 only on the ratio of speeds, nqe E = mg + kv. (1a) so the units of time and length are irrelevant, and there is no need to convert pixels to If the sphere falls, there are two cases—either the electric meters or frames to seconds (although such conversions may force plus the drag force balances the gravitational force: be generally valuable steps for students unpracticed with vid- eo analysis software). Terminal velocity is reached very quick- nqe E + kv = mg, (1b) ly, usually within a couple of sampling intervals. Occasionally or else the electric force plus the gravitational force balances a sphere makes a subtle but definite unanticipated change in the drag force: speed (Fig. 3) due to a spontaneous change in the charge on 300 THE PHYSICS TEACHER ◆ Vol. 60, April 2022

Fig. 5. The data from columns 10 and 11 of Table I. Line through data is least-squares regression fit constrained to pass through origin. Fig. 3. Detail of screenshot of Logger Pro analysis of I. It is evident that the data tend to fall into clumps corre- Event 9, episodes a, b, and c, which correspond to n = sponding to different values of n. Once all these data have 5, n = 4, and n = 3. been assigned values of n (rightmost column of Table I) a plot can be constructed (Fig. 5), and the slope s and its uncertainty (entered in first row of Table II) for the least-square linear fit computed by a spreadsheet, given the constraint that the fit Table II. Factors required to compute qe. Value Fractional uncertainty s 0.487 0.006 d (m) 3.1 10-3 0.05 mg (N) 2.8 10-14 0.05 V (V) 270 0.02 Fig. 4. The speed of unforced fall: <v0> = 31.59 pixels/ must pass through the origin, since by definition a sphere falls frame; standard deviation = 2.16 pixels/frame. at speed v0 when there is no electrical force. Since the slope equals the term in square brackets in Eq. (3), we have the sphere. We had not noticed this before we began tracking the sphere frame by frame, and this may be responsible for qe = s × mg × d/V. (4) some analysis errors in the past. The “PCC” video provides values for d, mg, and V (Table II), The CSV data file exported from Tracker requires aPmroi®n2o0r but not their uncertainties; they have been estimated based modification19 before it can be imported into Logger on the number of significant digits reported—two significant for analysis. In Logger Pro a point, click, and drag highlights digits implying a fractional uncertainty of 1% to 10%. I have each episode, and only two or three more clicks are required assigned an uncertainty of 5% to d and mg, and 2% (about to find the slope and its uncertainty. Spreadsheet software 5 V) to V. could also be used to find the speeds of the spheres but may not be so convenient as Logger Pro. Usable data from the 12 Assuming fractional uncertainties add in quadrature,we events are found in the first five columns of Table I. have a total fractional uncertainty of about 7%, and qe = (1.6 ± 0.1) × 10-19 C, consistent with the accepted value of 1.602 × 10-19 C. Results Discussion There are 13 episodes where the switch is set to “zero” or There are shortcomings to doing the experiment this else the sphere is uncharged, providing values for the unforced way—the data set is limited, the uncertainties in some of the speed v0 of the sphere (see Fig. 4). Although the constant experimental parameters can never be known, and quirks speed of the sphere in a single episode can be determined with such as the wide variation in values of v0 and v± for a given great precision, analyses of other episodes under seemingly n are impossible to investigate. Still, we value this approach identical conditions (i.e., charge and electric field) yield sig- because students are afforded the opportunity to grapple with nificantly different speeds. This is perplexing. Perhaps there real data and their uncertainties and ambiguities. In addition are some systematic uncertainties due to changing experi- it provides a review of the essential skills of using Newton’s mental conditions (e.g., air temperature). first law, drawing free-body diagrams, understanding the na- ture of the electric field, and the propagation of uncertainty. Values of 1 + v6/v0 are listed in the next column of Table THE PHYSICS TEACHER ◆ Vol. 60, April 2022 301

Frame-by-frame analysis (made possible by autotracking, likan oil-drop experiment,” Am. J. Phys. 73, 789–792 (Aug. without which it would be much too tedious) reveals a here- 2005). tofore unexpected richness of the video data set: distinct 10. PASCO’s apparatus includes an ionization source, a thermis- episodes of motion during a single video event. Thus one can tor, and LED illumination; Fisher Scientific’s unit has built- clearly observe the dynamic effect of a single electron, which in CCD microscope camera and timer. serves as convincing evidence that electric charge is indeed 11. Michel Gagnon, “Millikan's oil-drop experiment: A cen- quantized. tennial setup revisited in the virtual world,” Phys. Teach. 50, 98–102 (Feb. 2012). Acknowledgments 12. Physlet® Quantum Physics, Sec. 4.5: Exploring the Millikan I wish to thank my departmental colleagues, especially our Oil Drop Experiment (https://www.compadre.org/PQP/ chair, Nathaniel Cunningham, for their advice and assistance, quantum-need/section4_5.cfm). Descriptions of other com- the late Robert G. Fuller for assembling “PCC,” and the anon- puter simulations and animations may be found online. ymous reviewers for their helpful comments. 13. Xueli Zou et al., “Millikan movies,” Phys. Teach. 46, 365–368 (Sept. 2008). References 14. J. W. Robson, “Physics: Cinema Classics,” Comput. Phys. 6, 1. George Johnson, The Ten Most Beautiful Experiments (Alfred A. 556–557 (Sept. 1992). 15. See https://aapt.org/Store/upload/AAPTcatalog09_new.pdf Knopf, New York, 2008). “Millikan Experiment” is found on DVD F. 2. Isabel Bishop, Siyu Xian, and Steve Feller, “Robert A. Millikan 16. See https://handbrake.fr. 17. See https://physlets.org/tracker/ . and the oil drop experiment,” Phys. Teach. 57, 442–445 (Oct. 18. See https://www.compadre.org/osp/. 2019). 19. Since Logger Pro expects just one header row, you must 3. Images of Millikan’s lab notebook can be found at http:// delete one row of the column headings, and you may want to resolver.caltech.edu/CaltechLabNotes:LN_Millikan_R_2. change the headings and delete the extraneous x-column. If 4. Michael F. Perry, “Remembering the oil drop experiment,” Phys. you are editing in Excel®, you might convert numerical en- Today 60, 56–60 (May 2007). tries from “General” to “Number,” and change the number 5. Roy C. Jones, “The Millikan oil-drop experiment: Making it of digits in each value that will be exported to Logger Pro. worthwhile,” Am J. Phys. 63, 970–977 (Nov. 1995). 20. See https://www.vernier.com/product/logger-pro-3/. 6. “A Wish to Comply,” by Robert Frost, quoted by Roger K. We-   ber, “A poem on the Millikan oil drop apparatus,” Phys. Teach. William M. Wehrbein studied atmospheric physics at the University of 10, 155 (March 1972), and also by W. John Coletta and David H. Colorado Boulder and the University of Washington before he returned Tamres, “Robert Frost and the poetry of physics,” Phys. Teach. to his undergraduate alma mater to teach physics for 27 years. Since 30, 360–365 (Sept. 1992). his retirement he continues to volunteer in the junior-level laboratory 7. Steve Brehmer, “Millikan without the eyestrain,” Phys. Teach. course. 29, 310 (May 1991). Nebraska Wesleyan University, Physics and Astronomy Dept., 8. A. Papireo Jr., C. Penchina, and H. Sakai, “Novel approach to the oil-drop experiment,” Phys. Teach. 38, 50–51 (Jan. 2000). 5000 St. Paul Ave., Lincoln, NE 68504-2794; 9. K. Silva and J. Mahendra, “Digital video microscopy in the Mil- [email protected] Fermi Questions Larry Weinstein, Column Editor Old Dominion University, Norfolk, VA 23529; [email protected] w Question 1: Dinosaur killer crater w Question 2: Graduation speeches In 2003, the “Dinosaur Killer” asteroid crater was im- How much total time is spent listening to grad- aged for the first time (see National Geographic News, uation speeches in the U.S. each year? March 7, 2003). The crater is believed to be 100 km in radius and 1 km deep. What was the kinetic energy of Question suggestions are always welcome! the asteroid that made that crater? Express your an- swer in joules and in megatons (1 MT = 4 .10 J). Look for the answers online at tpt.aapt.org under “Browse,” at the very end of the current issue. For more Fermi questions and answers, see Guessti- mation 2.0: Solving Today's Problems on the Back of a Napkin, by Lawrence Weinstein (Princeton University Press, 2012). DOI: 10.1119/10.0009997 302 THE PHYSICS TEACHER ◆ Vol. 60, April 2022

A Visit to Kelvinside Thomas B. Greenslade Jr., Kenyon College, Gambier, OH In the summer of 1978 Sonia and Tom Greenslade paid a visit to the Department of Natural Philosophy of Glasgow University, situated in Kelvinside, a western suburb of the city of Glasgow. Tom had two aims, first to photograph early pieces of physics apparatus, and secondly to learn more about William Thomson, Lord Kelvin. Our host was J.T. Lloyd, the director of the Kelvin Museum. After our visit, he wrote an article, “Lord Kelvin Demon- strated,” for this journal.1 In it he noted that “about two years ago we were visited by an American Professor, Thomas B. Greenslade Jr. of Kenyon College in Gambier, Ohio. I remem- ber this with particular pleasure.” This was occasioned by my interest in his Kelvin water dropper electrostatic machine.2 He gave us the key to the apparatus cabinets and encouraged me to photograph at will. In this article I will show some of the pieces of apparatus with a connection to Kelvin and other physicists associated with the university. The River Kelvin passes close to the eastern side of the uni- versity as it travels southward to the River Clyde. We walked across a small bridge and passed the statue of William Thom- son, Lord Kelvin (1824-1907) (Fig. 1), in a small park with Fig. 1. Statue of Lord Kelvin in Kelvinside Park. skateboarders zooming around us. We entered the building housing the Department of Natural Philosophy and walked by Kelvin’s pitch glacier. In 1887, he constructed what appears to be a short and narrow set of stairs a few feet high and placed a quantity of pitch at the top. In the ensuing years the seemingly solid pitch slowly flowed down the steps.3 Kelvin’s name is familiar to many physicists. The absolute temperature scale that he devised has temperature in kelvins. Those who make precision electrical measurements will know the Kelvin bridge for alternating current work, and a different Kelvin bridge for measuring very small resistances. He worked on forms of telegraphy and Fig. 2 shows a telegraph instru- ment of the form devised by Charles Wheatstone that is in the Kelvin museum. He was the Professor of Natural Philosophy at Glasgow for 53 years, not retiring until 1899. He lived in a residence in one of the university buildings, and on our visit I took a picture of a cat sunning itself on his front porch. The demonstration apparatus was housed in a set of ele- gant glass cabinets abutting the main lecture hall. This was in a large and very tall room, with seating for the students in what looked like a small grandstand; you could walk all Fig. 2. Wheatstone’s telegraph instrument. around it. The “blackboard” fascinated me, for it resembled a wide and long rubber band that was held in place by rollers top and bottom. These were electrically driven, and I noticed that what had been written on it was now upside down when I walked behind it. The devices in the cabinets were certainly used by Kelvin for his demonstrations. There were two examples of Volta’s pistol, including the one in Fig. 3. This was “loaded” with a mixture of illuminating gas and air that was held in place with a cork. Presenting the insulated electrode at the side to a Fig. 3. Volta’s pistol. charged Leiden jar produced a spark that set off the mixture. DOI: 10.1119/5.0040276 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 303

Fig. 4. Savart’s wheel. Fig. 7. Joule’s tangent galvanometer. Fig. 5. Air mill. acoustical signal toward the students. To this day this would make a good student construction project, along with touch- Fig. 6. Joule’s calorimeter. ing the card to the spokes of a spinning bicycle wheel. The resulting loud bang certainly woke up sleepers at the back I have seen several examples of the air mill (Fig. 5) in my of the lecture room seats. scientific travels. It has fallen out of use, but is still an effective lecture demonstration. The little device, 10 to 15 cm tall, is Just as effective was the Savart’s wheel in Fig. 4. Turning placed on the pump plate of a vacuum system. The sliding the crank caused the two toothed wheels to rotate rapidly. connection at the top starts the two sets of vanes rotating rap- The lecturer (Kelvin) held the edge of a playing card against idly. The vanes whose surfaces are turned against the direc- the teeth. The card thus vibrated rapidly, sending out a loud tion of rotation rapidly come to rest because of air resistance, while the other set, with the blades set edge-on, continue to rotate. The bell jar is evacuated, the demonstration repeated, and now both vanes continue to spin. Students during Kelvin’s time never had the experience of putting a hand out the win- dow of a speeding car, and so had no feeling for air resistance. When we visited, the Kelvin museum was located in a se- ries of glass cabinets around the walls of the staff dining room. An inconspicuous item was a short section of an Atlantic ca- ble, a reminder that Kelvin had designed the sensitive siphon galvanometer that made it possible to receive the very faint signals. A more personal Kelvin object was the French horn that he played for recreation. This was of the original form, without valves, and to play music in other keys a variety of “crooks,” small segments of brass “plumbing” were inserted. The Glasgow brewer James Prescott Joule was an indepen- dent scientist who kept in touch with Kelvin and other mem- bers of the local scientific establishment. The calorimeter that Joule used with his experiments4 on the mechanical equiva- lent of heat (Fig. 6) is on display in the museum. This contains a set of paddle wheels that were used to stir the water inside the calorimeter. The museum also displays a tangent galva- nometer (used to measure electric current) in Fig. 7; the label next to it notes, “This instrument was used by Joule in his re- 304 THE PHYSICS TEACHER ◆ Vol. 60, April 2022

Fig. 8. Stirling’s hot air engine. searches and was presented to Lord Kelvin by Joule’s son.” At the present time interest has begun to revive in the hot air engine of the type developed by the Scottish clergyman and engineer Robert Stirling (1780-1878) in the early years of the 19th century. Figure 8 shows one of Stirling’s engines. When I looked up “Stirling Engine” on the internet, I was amazed to see that this piece of apparatus was now on display at the Hunterian Museum in Glasgow. We retain vivid memories of our visit to Glasgow, includ- ing driving up the west shore of Loch Lomond. We stayed in a bed and breakfast, where we joined a couple of lachrymose Scotsmen who were watching Scotland lose badly in a World Cup game. References 1. J. T. Lloyd, “Lord Kelvin demonstrated,” Phys. Teach. 18, 16–24 (Jan. 1980). 2. Builders of the Kelvin water dropper electrostatic machine should look at J.T. Lloyd’s description of his large and amazing version of it in Ref. 1. 3. There is a picture of the pitch glacier in Ref. 1 (Fig. 9). 4. Thomas B. Greenslade Jr., “Nineteenth-century measurements of the mechanical equivalent of heat,” Phys. Teach. 40, 243–248 (April 2002). Kenyon College, Gambier, OH; [email protected] THE PHYSICS TEACHER ◆ Vol. 60, April 2022 305

Five Surprising Facts About Molecules of Water and Air A. James Mallmann, Milwaukee School of Engineering, Milwaukee, WI This article presents answers to five questions about Approximately how many air molecules inhaled by molecules of water and air. In Chapter 1 of Volume 1 of a person today were exhaled during one minute by The Feynman Lectures on Physics,1 Richard Feynman Isaac Newton? suggests that: “If in some cataclysm all scientific knowledge This is a version of a famous question that usually refers were to be destroyed, and only one sentence passed on to the to Caesar’s last breath, but sometimes refers to the last breath next generation of creatures, what statement would contain of other famous people or of a dinosaur. Entering “Caesar’s the most information in the fewest words? I believe it is the last breath” in an internet search engine will typically result atomic hypothesis … that all things are made of atoms ….” in connection to more than 100,000 websites. Water molecules are made of hydrogen and oxygen atoms, Breath is also the title of a book3 by Sam Kean Caesar’s Last and 99% of molecules in air are diatomic nitrogen and oxygen ing the Secrets of the Air Around Us. subtitled Decod- molecules—each made up of two atoms. The answers to the During one minute the typical volume of air exhaled by questions presented provide ways to think about how small a human is approximately 14 L. An ideal gas law calculation molecules are, the surprising abundance of hydrogen mole- shows that the number of air molecules exhaled in one min- cules in the atmosphere, and the damage that can be caused ute is approximately 3.43 1023. If that number of molecules by a large collection of rapidly moving air molecules each with were uniformly distributed throughout Earth’s atmosphere, a mass of less than one ten thousandth of a billionth of a bil- assumed to extend 10 miles above Earth’s surface, there would lionth of a gram. be 40 molecules of air exhaled by Newton in each liter of air. Since the typical volume of air inhaled by a person is one How long would it take to remove all the molecules half-liter, a person today would inhale in a single breath 20 air in a drop of water if one million molecules were molecules earlier exhaled during one minute by Newton. But, removed each second? although assumed for this calculation, air is not uniformly The volume of one typical water drop is one-twentieth of dense. According to the Law of Atmospheres4 air density de- a cubic centimeter. For this calculation, a volume of 0.0500 creases exponentially with altitude. The air density at sea level cubic cm and a mass of 0.0500 g are used. The mass of one wa- is more than seven times greater than the density 10 miles ter molecule, which is equal to the molecular weight of water above Earth’s surface. The number of inhaled air molecules (18.0 g/mole) divided by Avogadro’s number, is approximately in one breath earlier exhaled by Newton would therefore be 0.000000000000000000000030 g—which shows why scientific greater than 20. notation is used for calculations that involve very small or very large numbers. How many water molecules would be evaporated To three significant digits the mass of a water molecule is in one microsecond from an area of one square 2.99310-23 g. The number of water molecules in a drop of wa- millimeter of the surface of the water in a cup at ter, which is equal to the mass of a drop divided by the mass of one water molecule, is 1.6731021. room temperature? The constant rate of decrease in the mass of the water at The time to remove all the molecules from one drop, which room temperature in a 45-mm diameter Styrofoam cup due is equal to that number of molecules per drop divided by the to evaporation was measured5 to be 4.4310-5 g/s. The rate of one million per second rate of removal, is: ndeucmrebaesrebpyetrhuen3i.t0a3re1a0-w23asg2m.8a3ss10p-e1r4gm/oµlsec/mulme g2i.vDesivtihdeinragttehat at which water molecules leave the surface per unit area by 1.6731015 s —53 million years. This thought experiment assumes that no evaporation of the evaporation. water occurs.2 Although the volume of the water in the cup appears un- The diameter of a spherical water drop with a volume of changed over more than an hour, during each microsecond 0.0500 cm3 is 4.57 mm. As water molecules are removed from approximately one billion water molecules leave each square the drop, the drop gets smaller. But after 100,000 years of millimeter of the surface by evaporation. removing one million molecules per second, the diameter of the drop, to three significant digits, would still be 4.57 mm—a Hydrogen molecules make up 0.000055% of air. decrease of 0.003 mm. How many hydrogen molecules are in one cubic mil- Here is another measure of the number of molecules in one limeter of air? drop of water: If the molecules were placed in a straight line If 10 times the average speed of the molecules in a planet’s one millimeter apart, the line would be more than 176 light- atmosphere is greater than the escape velocity for the planet, years long—more than 20 times the distance from Earth to the the molecules will escape the planet’s atmosphere.6 Ten times brightest star Sirius. the average speed of hydrogen molecules in Earth’s atmo- sphere is 1.7 times the escape velocity for Earth, assuming an 306 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/5.0051087

average temperature of 288 K for the atmosphere. Ten times The kinetic energy of an 80,000-lb (36,000-kg) semitrailer the average speed of nitrogen molecules is less than one-half truck with a speed of 60.0 mi/h (26.8 m/s) is 1.293107 J. The the escape velocity for Earth. Comparison of these speed ra- number of 80,000-lb semitrailer trucks that would have the tios is consistent with the fact that nitrogen molecules make same kinetic energy as the air molecules in one cubic kilome- up 78% and hydrogen molecules make up only 0.000055% of ter of air in a category 4 hurricane is equal to the ratio 2.363 Earth’s atmosphere—a percent ratio of 1.4 million to 1. Hy- 1012/1.29 3107, which is equal to 183,000. Imagine the damage drogen is usually referred to as a trace component of Earth’s that could be caused by an 80,000-lb, 60-mi/h semitrailer truck atmosphere. that crashed into a building. The wind in a cubic kilometer in a category 4 hurricane would have the energy to do the damage of An ideal gas law calculation shows that for an atmospheric 183,000 60-mi/h semitrailer trucks. temperature of 288 K, there are 2.531016 molecules per cubic mm. The number of hydrogen molecules in one cubic mm References is 0.000055% of that number: 14 billion. Numbers are inter- 1. Feynman, Leighton, Sands, The Feynman Lectures on Physics De- esting. Hydrogen molecules—a trace component of Earth’s atmosphere—are present in a concentration of 14 billion per finitive Edition, Vol. 1 (Pearson Addison-Wesley, 2006), pp. 1-2. cubic mm. 2. If evaporation occurred, all the molecules would move from the How many 18-wheel, 80,000-lb semitrailer trucks drop to the surrounding air in about 20 minutes—with an initial with a speed of 60 miles per hour would have the removal rate by evaporation of about 1400 billion molecules per same kinetic energy as that of the molecules in microsecond. one cubic kilometer of air in a category 4 hurri- 3. Sam Kean, Caesar’s Last Breath (Back Bay Books / Little Brown cane? and Company, 2017). 4. R. Serway, Physics for Scientists and Engineers, 4th ed. (Saunders At a temperature of 300 K, the number of air molecules per College Publishing, 1996), p. 600. cubic km is 2.4431034—78% are nitrogen molecules and 21% 5. The following data were taken for the water in a small Styrofoam are oxygen molecules. cup initially containing 10 grams of water at room temperature: The mass of the water as it decreased due to evaporation was The range of speeds for a category 4 hurricane is 209— measured by the author using a scale that could measure the water 251 km/h. The middle of that range is 230 km/h or 63.9 m/s. mass to the nearest 1000th of a gram. In one cubic km of air the total kinetic energy of 1.9031034 6. Theo Koupelis, In Quest of the Universe, 6th ed. (Jones and Bartlett nitrogen molecules and 5.1231033 oxygen molecules with Learning, 2011), p. 192. speeds of 63.9 m/s is 2.3631012 J. Help Build a Physics Community! Contribute - Personalize - Share ComPADRE creates, hosts, and maintains collections of educational and community resources focused on the needs of specific audiences in Physics and Astronomy Education Explore the ComPADRE Collections: http://www.compadre.org/portal/collections.cfm THE PHYSICS TEACHER ◆ Vol. 60, April 2022 307

iPhysicsLabs Jochen Kuhn and Patrik Vogt, Column Editors Ludwig-Maximilians-Universität München (LMU Munich), Faculty of Physics, Chair of Physics Education; [email protected] Institute of Teacher Training (ILF), Mainz, Germany; [email protected] Recording a resonance frequency and reaches its maximum when the excitation fre- curve with smartphones and quency and the natural frequency just match—this is called wine glasses resonance. Patrik Vogt, Institute of Teacher Training (ILF), Mainz, Germany; Setup and execution of the experiment [email protected] In order to perform the experiment, we must first deter- Lutz Kasper, University of Education Schwäbisch Gmünd, Germany; [email protected] mine the natural frequency of the glass used in a preliminary test. We strike the glass with a wooden spoon and display Numerous experiments on acoustics have already been the frequency spectrum of the resulting sound signal with a described in this column, e.g., on the different types of suitable app (Fig. 1). For the glass used here, we find a funda- sound1 or on acoustic beats.2 The topic of cavity resonance and mental of 603 Hz, which thus corresponds to the first natural the determination of the speed of sound from the resonance frequency of the glass. If we want to excite the wine glass to frequencies of various tubes,3 glasses,4 and bottles5 has also vibrate exclusively with sound waves, we should do it at this been addressed several times. A topic that has not yet been considered is the recording of a resonance curve. We would like to present here an experimental possibility with very simple de- vices. Apart from two smartphones, all you need is a wine glass. Motivation of the experiment Fig. 1. Experimental determination of the natural frequency of It is often claimed that trained singers are able to break the glass used (App: Schallanalysator6). glasses just by using their voice, and there are numerous videos Fig. 2. Experimental setup for recording a resonance curve on a circulating on the internet that would also like to make us be- wine glass. lieve this. A physical explanation that is often heard seems quite plausible: You just have to excite the glass acoustically at its nat- frequency for the best possible success. ural frequency. Then the glass will vibrate particularly strongly. To check this, we use a smartphone or tablet computer If you hold this tone long enough, the oscillation is increasingly amplified. The result is a resonance catastrophe, causing the with a tone generator app. Here we used the Audio Kit app, glass to break. which allows us to generate tones with an accuracy of 1 Hz.7 At a distance of a few centimeters from the wine glass, we ex- In fact, the destruction of a glass in the described way occurs posed it to sound for about seven seconds. Then we switched when it is exposed to sound from a tone generator. In contrast off the sound generator and measured the sound pressure to the human voice, the generator is able to hold the frequency level of the sound now generated by the wine glass itself (Fig. of the generated sound exactly over a longer period of time. 2). The free app phyphox8 was used here, which can also be Also, with the aid of an amplifier, a significantly higher sound used for sound generation. We have applied the described pressure can be achieved. We would now like to carry out the experiment on a small scale and will analyze the phenomenon of resonance in more detail. Theoretical background Once a body is excited to vibrate, it performs free vibrations with a characteristic frequency. This frequency depends only on properties of the body and is called natural frequency. As a result of friction, the amplitude of a free vibration decreases and the body takes its rest position after some time. If, on the other hand, the oscillation of a body is maintained by periodic energy supply from outside, it performs forced oscillations. An example of this is a child’s swing, in which energy is periodi- cally supplied to the oscillating system by pushing on it or by a clever shift of the child’s own center of mass. The frequency of the energy supply is called the excitation frequency. The amplitude of an excited oscillation depends on the excitation 308 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0009999

iPhysicsLabs Fig. 3. Time characteristic of the amplitude for an excitation with 614 Hz. procedure for the natural frequency of 603 Hz as well as for the Fig. 4. Graphical representation of the measurement series. integer frequencies in the range from 593 Hz to 614 Hz. then can the glass be excited to strong vibrations and can be Experimental result destroyed. Due to our anatomy, however, we are not able to The course of the amplitude during the entire process is hold a frequency exactly over a longer period of time. And shown in Fig. 3. The sudden increase in amplitude marks even if we were, the sound pressure would be far from suf- the turning on of the tone generator app, which produced a ficient. While a well-trained opera singer with an accurate tone of constant amplitude for about seven seconds. After tone can easily make a wine glass vibrate with her voice, she the sound is switched off, the curve immediately drops to the cannot destroy it. sound pressure level caused by the glass. This value is read and serves us as a measure of the excitation of the vibration. The References fact that the sound pressure level here is negative at around 1. J. Kuhn and P. Vogt, “Analyzing acoustic phenomena with -63.7 dB should not matter here. Above the hearing threshold, a smartphone microphone,” Phys. Teach. 51, 118–119 (Feb. one would actually expect exclusively positive level values, at 2013). least when the app has been calibrated correctly. However, we did exactly without this calibration since the absolute levels do 2. J. Kuhn, P. Vogt, and M. Hirth, “Analyzing the acoustic beat not really matter for the experiment. with mobile devices,” Phys. Teach. 52, 248–249 (April 2014). The result of the whole measurement series is shown in 3. M. Hirth, J. Kuhn, and A. Müller, “Measurement of sound Fig. 4. We can see from the resonance curve there that the ex- velocity made easy using harmonic resonant frequencies with citation of the wine glass actually is particularly pronounced everyday mobile technology,” Phys. Teach. 53, 120–121 (Feb. at the natural frequency (obviously this is 604 Hz and not 603 2015). Hz). The further we move away from the natural frequency, the quieter the wine glass continues to vibrate after the tone 4. M. Monteiro, A. Marti, P. Vogt, L. Kasper, and D. Quarthal, generator app is switched off. If we apply a frequency to the “Measuring the acoustic response of Helmholtz resonators,” wine glass that deviates from the natural frequency by at least Phys. Teach. 53, 247–249 (April 2015). 20 Hz, there is no longer any noticeable vibration excitation. 5. M. Monteiro, C. Stari, A. C. Marti, “A bottle of tea as a uni- versal Helmholtz resonator,” Phys. Teach. 56, 644–645 (Dec. 2018). 6. Schallanalysator, iOS: https://ogy.de/Schallanalysator-iOS; The experiment shows that in order to break the glass, we Android: https://ogy.de/Schallanalysator-Android. would really have to hit its natural frequency exactly. Only 7. Audio Kit, iOS: https://ogy.de/Audio-Kit. 8. phyphox, iOS: https://ogy.de/phyphox-iOS; Android: https:// ogy.de/phyphox-Android. THE PHYSICS TEACHER ◆ Vol. 60, April 2022 309

little gems Christopher Chiaverina, Column Editor 4111 Connecticut Trail, Crystal Lake, IL 60012; [email protected] Simple demonstrations of refraction hide some deeper physics Andrew Morrison, Joliet Junior College, Joliet, IL Over the past few years there have been several viral vid- eos posted online that have demonstrated the so-called “Reversing Arrow Illusion.”1,2 This simple demonstration is conducted by putting a clear glass in front of a piece of paper that has had arrows drawn on it. When the glass is filled with water, the arrows appear to reverse direction. The demonstra- tion is shown in Fig. 1. When any explanation of the physics is offered in the (a) (b) online posts of this demonstration, usually the explanation Fig. 1. (a) Empty drinking glass in front of an index card with discusses the phenomenon of refraction, which causes light arrows drawn on it. (b) Same drinking glass, now filled with water to bend, and thus causes the arrows to reverse the direction in front of the same card. they are pointing. While this type of description is not wrong, it is incomplete. (a) (b) To illustrate that the concept of the effects of refraction Fig. 2. (a) An empty glass vase with a rectangular cross section. due to the addition of water alone is not enough, the drinking (b) The same vase being filled with water. No reversal of the glass (with a circular base) is replaced with a glass vase having arrow direction is observed. a rectangular base and flat walls. Figure 2 clearly shows that the arrows are not appearing reversed as the water is poured (a) (b) into the vase. Fig. 3. (a) Photo of a bear swimming in a zoo enclosure taken with The shape of the vessel containing the water is clearly also a large angle of incidence to the glass surface. (b) Photo of the affecting the path that the light takes from the arrow to the same bear in the same enclosure taken with a very small angle observation location. In the case of the drinking glass, the of incidence. circular cross section of the water column is acting like a con- vex lens and causes the reversal of the arrow directions. The shape of the vessel can also make the image appear inverted in some cases.3 For an in-class demonstration, it would be useful to have students draw ray diagrams and make predictions about the required object and image distances in order to see the rever- sal of the arrows. Sometimes students forget that the cause of the bending of the light rays in a lens is due to the refraction of light incident on the curved surface of the lens. This demonstration is a way to remind students of the connection between refraction and lens behavior. Of course, in the case of the vase with flat walls, refraction is still occurring. A dramatic way of illustrating the effect of refraction in the case of flat clear walls is shown in Fig. 3. Viewed from an angle with respect to the normal of the glass wall, the bear’s head (above water) appears separated rf(ribgo)hmt its body (below water.) Compared to the photo (on the in Fig. 3) showing the bear photographed such that the camera is perpendicular to the glass wall, the effect of refrac- tion through the water is quite dramatic. Many examples of this type of refraction effect can be found online.4 In all of these examples, it is important to remember the ef- fect of the curved (or flat) surfaces in addition to the index of refraction of the water. The refraction effect depends on both! 310 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0010000

References gems 1. “Amazing Water Trick – Amazing Science Tricks Using Liquid,” 3. J. Lúcio Prados Ribeiro, “A glass of wine a day does not keep YouTube, https://www.youtube.com/watch?v=G303o8pJzls, optics away! Reflection and refraction images in wine glasses,” accessed Jan. 14, 2022. Phys. Teach. 51, 506 (Nov. 2013). 2. A search on Twitter reveals many examples of this demonstra- tion video recorded and posted online: https://twitter.com/ 4. Perhaps the most widely shared exemplar of this type of re- search?q=refraction%20arrows&src=typed_query&f=top . fraction effect can be found through a Google image search of “refraction of light funny” as seen here: https://bit.ly/3qsTkhe. And the Survey Says ... Susan C. White, Column Editor American Institute of Physics Statistical Research Center College Park, MD 20740; [email protected] The impact of the COVID-19 pandemic on faculty members’ time allocation In the spring of 2020, many high schools and universities transitioned to online course instruction. As one might expect, this had an impact on physics and astronomy faculty members’ allocation of time. We sent a survey to faculty members at randomly selected physics and astronomy departments in the spring of 2021. We asked them to compare the time spent on various tasks prior to the pandemic with the time spent in the spring of 2021. Seven fac- ulty members in 10 (71%) reported spending more time on teaching and advising, and about six faculty members in 10 (58%) reported spending less time on research and scholarship. This graph comes from our report Changes in Time Allocation During the COVID-19 Pandemic for Full-Time Faculty in Physics and Astronomy. The footnote references additional figures that look at changes by the highest degree the department awards. For those interested, that report is available at https://www.aip.org/statistics/reports/changes-time-allocation-during-covid-19-pandemic-full-time-faculty. Next month we will look at the impact of the pandemic on faculty members’ work-life balance. Susan White is Director of the Statistical Research Center at the American Institute of Physics. If you have any questions or com- ments, please contact her at [email protected]. DOI: 10.1119/10.001000 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 311

AstroNotes Column Editors: Donald A. Smith, Guilford College, Greensboro, NC; [email protected] Janelle M. Bailey,Temple University, Philadelphia, PA NITARP, the NASA/IPAC As far as we know, we are unique in providing the follow- Teacher Archive Research ing combination of qualities: Program • Our program is aimed at educators (not students), L. M. Rebull, Caltech-IPAC, Pasadena, CA though participants are encouraged to involve students in the entire process. In practice, most—but not all— Have you ever wanted to get into astronomical data? participants start working intensively with students a few months into the program, in preparation for the IPACITmeaecahneRrEAArcLhLiYveinRteosaesatrrcohnPormoigcraalmda(tNa?ITTAhRe PN)A1 SgAet/s summer visit. Some teachers feel they learn better when teachers involved with real astronomy data and research. We not side by side with students, which is fine. Others in- partner small groups of (largely) high school educators with volve students as early as possible in the program. a professional astronomer mentor for an original research project. The educators incorporate the experience into their • We select participants from a nationwide application classrooms and share their experience with other teachers. process. The program runs for a full year, January through January. Applications are available annually: posted in May and closed • Our program involves educators for about a year (Janu- in September. ary-January). (Long-term interactions have been shown to have more impact than short-term interactions; see Since the advent of NGSS, educators have been asked to discussion in Refs. 4 and 5.) support authentic science experiences in high school and middle school, an experience that they themselves may never • Our participants do real research. NO cookbooks! And have had.2 NITARP provides an authentic science experience our participants are not just “along for the ride”—they for teachers. We work primarily with educators specifically do the analysis and are involved in the entire process, because of the leveraging effect—by changing the way a teach- from writing the proposal through presenting the re- er thinks about science, scientists, astronomy, data, etc., we sults. impact the students they have this year, next year, and through the rest of their careers. We reach students through our teach- • Our participants present results in the same AAS ses- ers. sions as professional astronomers, and must “hold their own” in that domain. The program echoes the entire research process, from proposal to presenting the results at a professional confer- Teachers come to NITARP because they are looking to ence.3 Participants get three trips paid for by the program. learn and grow4 (in Ref. 5 at least 80% tell us that this is a pri- The first trip is attending an American Astronomical Society mary motivation). Unprompted, 14% of our alumni used the (AAS) winter meeting in January to meet their team and start words “life changing” when describing the impact of NITARP learning about their project. The second trip is four days at on their lives.5 Some of this change means “rethink[ing] my\\ Caltech/JPL in Pasadena, CA, during the summer to inten- entire approach to science education” because real science has sively work on their project as a team (the program also pays no cookbooks, and some of this change comes from being ex- for up to two students per teacher to participate; teachers can posed to new educational opportunities and/or jobs outside raise money to bring two more). The third trip is to attend a the classroom. second AAS meeting (in January of the next year) to present their results; again, the project pays for up to two students We typically have more than five applicants for each open per teacher to come as well. The teams work remotely for the position, so competition is fierce. This demand is probably duration of the program. Educators then share the experience because the NGSS asks a lot of teachers, and, as a result, with at least 12 hours of PD/workshops held locally, regional- teachers seek out professional development opportunities like ly, or nationally. this. Each team consists of three to four new educators, a men- As a result of the pandemic, NITARP did not solicit appli- tor teacher (who has been through the program before), and cations for new teams in 2021. While much of the work is a mentor astronomer. Most educators who have gone through done remotely (and is therefore 100% compatible with the program have been high school classroom educators, distance learning), the trips are an integral part of the ex- though we have also had middle school, community college, perience, and we did not want to accept new teams without planetarium, and informal educators participate. knowing whether they could travel. As of this writing, we are running normally in 2022. Look for applications for the 2023 class in May 2022. 312 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0010004

References AstroNotes 1. See http://nitarp.ipac.caltech.edu. 2. See, for example, these articles and references therein: L. Re- Program (NITARP),” Rob. Telesc. Stud. Res. Educ. 1, 171 (2018), https://ui.adsabs.harvard.edu/abs/2018RTS- bull, “Authentic research in the classroom for teachers and RE...1..171R abstract . students,” Rob. Telesc. Stud. Res. Educ. 1, 21 (2018), https:// 4. L. Rebull et al., “Major outcomes of an authentic as- ui.adsabs harvard.edu/abs/2018RTSRE...1...21R/abstract; tronomy research experience professional development J. Krim et al., “Models and impacts of science research experi- program: An analysis of 8 years of data from a teacher ences: A review of the literature of CUREs, UREs, and TREs,” research program,” Phys. Rev. Phys. Educ. Res. 14, 020102 CBE Life Sci. Educ. 18 (4), (2019), https://doi.org/10.1187/ (2018), https://doi.org/10.1103/PhysRevPhysEdu- cbe.19-03-0069; D. Hemler and T. Repine, “Teachers do- cRes.14.020102. ing science: An authentic geology research experience for 5. L. Rebull et al., “Motivations of educators for partici- teachers,” J. Geosci. Educ. 54 (2), 94-102 (2006), https://doi. pating in an authentic astronomy research experience org/10.5408/1089-9995-54.2.93. professional development program,” Phys. Rev. Phys. 3. L. Rebull et al., “The NASA/IPAC Teacher Archive Research Educ. Res. 14, 020248 (2018), https://doi.org/10.1103/ PhysRevPhysEducRes.14.010148. Figuring Physics March 2022 Answer DOI: 10.1119/10.0010002 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 313

talkin’ physics James Lincoln, Column Editor PhysicsVideos.com, Newport Beach, CA 92658; [email protected] Get dizzy: A kinesthetic lab Fig. 1. Students will learn what 1 rad/s is on angular speed by spinning at this tediously slow rate. Later they discover that 1 Hz is quite fast. James Lincoln, Woodside High School, Woodside, CA; [email protected] spins while they are measuring the time. The students can be somewhat inventive and come up with their own methods When we begin our unit on rotational dynamics, should of measuring these spins. Smartphone apps can also be em- we expect students to understand angular speed and ployed (see below) but may interfere with the purity and joy angular acceleration without any prior experience or intu- that comes from spinning with wild abandon. ition? In this article, I describe a lab in which students are instructed to spin with different angular speeds, or angular Results frequencies, and in different units such as rad/s, rpms, and Hz The students discover immediately that 1 rad/s is terribly or cps. I have found that after having students perform these spins, they have a better grasp of radians per second as a unit slow, and 1 Hz is actually quite fast. In the last step, where a of angular speed and how it compares with Hz or rpms. Going student spins as fast as possible, we learn to define “very fast” further, this article also includes tips for using mobile phone as over 15 rad/s. (I once had a ballerina student who could apps to get more accurate measurements. spin at over 3 Hz or about 20 rad/s!) Thus, like 1 m/s, the val- ue of 1 rad/s is “slow” and similarly anything over 6 rad/s is Pre-lab “quite fast.” For the students to perform the lab, they must already be After the lab is complete, it is now a good time to introduce proficient in converting cycles to radians, degrees to radians, the symbols that will come in the angular speed unit: and revolutions per minute to hertz, etc. Initially I have the and . Only now that the students have a good intuition for students learn to convert between radians and arc lengths, rad/s will these symbols make sense and equations such as convert radians to degrees, and convert cycles into radians. Some essential problems are change 90 degrees to radians, = 0 + t come naturally to them. convert 2 radians to degrees, 5 cycles to radians, and so on. After this, they can begin to understand the various units for Further investigations angular speed. A more accurate method for measuring angular speed can Examples: also be achieved using a smartphone accelerometer,2,3 for 1. An airplane propeller spins 200 times in 1 second. De- example, using the phyphox app (Fig. 2). However, a more termine the frequency in rpm and the angular speed . effective way to do this is by using the magnetometer (Fig. 2. A fish swims around its bowl four times every minute. 3). Because Earth’s magnetic field vector hits your phone at Determine the angular speed. different angles as you rotate, you can measure the period of 3. What is the angular speed of Earth in radians per year? your spin and thus the frequency by examining one axis of magnetic field at a time. The lab instructions1 In this lab, students are instructed to spin (Fig. 1), at vari- Another way to measure for accurate angular speeds is to make a slow-motion video of the spinner or spinners. This ous speeds. First at 1 rad/s. How does that feel? Next at can provide a tiebreaker in case you are trying to settle who 1 Hz; how does that feel? 20 rpm, etc. What would it be like to spins the fastest. spin at 100 rpm? Is this even possible? A motivating phenomena-based question might be, “How After they have had some experience with these given fast do you have to spin to become dizzy?” Requiring students values, the students are next instructed to spin as fast as they to answer in rad/s can ensure that they come to adopt this new can and measure this in units of cycles/s and rad/s. A fun unit and become comfortable using it. incentive can be to have the students “race” and find out who can spin five times the fastest. Safety Warning: Because they might fall, it is a good idea to perform this lab outside, on the grass, or on a sports field. Measuring the rate of spin is accomplished by having a partner with a stopwatch count out the seconds or count the 314 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0010003

talkin’ physics Fig. 2. A screenshot from the phyphox app. The author spins at about 1 Hz as reported by the accel- erometer. In each cycle the phone was tipped toward a stationary object (in my case a desk lamp). Fig. 3. The author spins himself into nausea at about 2 Hz. Thanks to Earth’s constant magnetic field we can measure the maximum rate of rotation to be 1 cycle/0.5 s. On a smartphone the z-axis is directed toward the user’s face, thus it is the best choice for this experiment, since the student’s face is changing its direction as they spin. References 1. The full angular kinematics unit is included as an online ap- pendix. This includes the lab handout. See TPT Online, http:// dx.doi.org/10.1119/10.0010003 under the Supplemental tab. 2. A. Kaps, T. Splith, and F. Stallmach, “Shear modulus determina- tion using the smartphone in a torsion pendulum,” Phys. Teach. 59, 268 (April 2021). 3. M. S. Wheatland, T. Murphy, D. Naoumenko, D. van Schijndel, and G. Katsifis, “The mobile phone as a free-rotation laborato- ry,” Am J. Phys. 89, 342–348 (April 2021). THE PHYSICS TEACHER ◆ Vol. 60, April 2022 315

just physics? Column Editors Deepak Iyer, Bucknell University, Lewisburg, PA Shannon Wachowski, EdReports Rooted in their reality: Driving questions before, the anchoring phenomena approach is dif- question boards as a tool for ferent, as instead of focusing on a short question that can be equity answered with a quick derivation, students are presented with a real-world occurrence that is more complex and requires Matt Richard, Olathe North High School, Olathe, KS several concepts to arrive at a solution. Phenomena should be accessible to all students and relate to their everyday lives so This year was my first in a high school classroom. Prior tthheaitrsetuvdereyndtsaycalannsgeueargeele.1v4aSntcuedaenndtseanrgeaagbeleintodibsrcionugrtsheeuirsipnegr- to this I taught nine years in college across all levels of physics. I love teaching and physics. But the longer I’ve been sonal experiences to the forefront and are provided the agency a physics educator, the more I have noticed that physics is taoncahskorqiunegsptihoennsotmo menoav1e5 their understanding forward. The often thought of as a “tough” course meant to “weed out” approach gives the students some- students, and that this perception does not impact all popu- thing to come back to and ground their learning. lpsianirmteoiqogilunraaisrtmieeeqnssu.ta4rar,y5lelFyrw.auRtereltalshcdoeioabr,clstugehramevpeedsdniisn.t2pe,gd3arr,T1aithdayniusidanitscifoeeonxmnatracralaeetsre,tbsBsaflttraaeocrdmkkb,lyaSynTwgdEeitnMHhditeshr-e One way that students can equitably engage with a(DncQhBor)-.16 ing phenomena is through a driving question board After experiencing an anchoring phenomenon or being pre- sented with a guiding question, students write their personal pexapnliacinsteuddbenytpsrceopmarpalteitoinngledveeglsreoerssioncSioTeEcoMnofimeldicssctaantunso.1t,6be questions in their own voice on Post-it® notes. Students then take turns reading their questions and placing them on the Research suggests that underrepresented populations seek board. Similar questions are grouped by the class and themes degrees that allow them to help communities, and the com- emerge. These themes or overarching questions are then pprleetsieonnteddisicnretphaisnwcyayi.s7e,8vidence that STEM fields are not being used to help students figure out what subquestions need to be answered to understand the phenomenon and create a The longer I taught, the more I noticed that I was teaching plan for learning. The boards are present in the classroom students who knew they wanted to be scientists and I was throughout the unit and are constantly referenced, reinforcing missing those that did not know they could be scientists. Stu- student-driven sense-making. dent perceptions of themselves as scientists is pivotal in their In subsequent storyline routines, students figure out what choice to cSoTnEtMinueexpinersiceinencecsetsoopitroisdnuecceefsustaurryetsocbieunitldistpso.9sIi-n they need to know (problematizing), conduct the investiga- tive early tions, organize their data in a way to frame a scientific argu- the transition to the high school setting I was forcing myself ment n(peuxttt(innagvtihgeaptiioence)s.1t2oTgehtehefor)c,uasnids then figure out where to relearn what it meant to learn physics and needed to put to go on the students and myself back into the role of a novice. I was given three classes how they make sense of the world. It allows students to take of AP physics and two classes of physical science to teach. The the wheel of their own learning and provides equity of voice notions that “physics was difficult” and “physics is not for both in the questions they ask and the questions they solve. everyone” were voiced from both students and parents within When an anchoring phenomenon is relevant, embedded in twhiethfiirnstmwyeetekaacnhdinsgo.m10ething I wished to deliberately contend the students’ culture, and students are given the opportunity to engage with the phenomenon in terms of their own experi- In my previous position teaching physics for engineering esenncsees,otfh.1e7y,1s8tart to see the science they are intended to make students, my colleagues and I would strive to tie-in real-world examples within all of our units. Physical phenomena are This was a lot to take in, but I was and am optimistic. The everywhere; surely letting students see how the numbers and task of implementing the “new-to-me” procedures that would concepts aligned with specific examples around them would promote student voice and identity in science started as part give them a clear idea of the importance and usefulness of the of the PhysTEC work I had been part of through the Uni- subject? I presented a carefully curated collection of examples versity of Kansas. Through our Teacher Advisory Group, we and situations and still got asked, “How does this relate to established a community of practice where we share what has me?” I was missing scaffolding for my students to share in the happened in our classrooms and co-design place-based, inter- development of their own relevant learning pathways. The est-driven units. The development of this virtual professional explicit framing of eKq-u1i2tySocfievnocieceEadnudcaptrioacnti(cFeraismceawlleodrko)u.1t1in learning community has spread the cognitive lift of redesign- the Framework for ing what physics could be for students. Together we were seek- In looking at the routines common in phenomena-based ing to answer our own anchoring phenomenon of: Why does instruction as described in the Framework, it became clear that in order to best meet the needs of students, the balls and equitable access in physics matter? ramps would have to veer off course. When the time came to try my first attempt at storylining and setting up a phenomenon, I chose storm tracking to look to tSrtaonrsyfolirnminoguprrolevairdneidnagn.12a,v13enAusetoforrylminyesitnusdtreunctstiaonndalmmyosedl-f at charges and motion in physical science. How and why do hurricanes change their category rating as they travel to- el for a unit involves several routines (anchoring phenomena, wards and across land? It was a step and I used phenomena, navigation, putting the pieces together, and problematiz- but was not ready to attempt a driving question board. I was Finrga)mthewatoermk.b11edWihdielaesIfhoardcouhseerdehnoceokans dtoegqeutistytufdroenmtsthaseking not ready to let students take complete ownership. Students were still quiet, a little more engaged in how things kept ty- 316 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0010005

just physics? ipnrgesbeanctk. Ftoorththeepnheexntormouenndon, w, beuutseeqduditryonofevdoeilciveewrya1s9naostmyeyt 4. E. Makarova, B. Aeschlimann, and W. Herzog, “The gender gap in STEM fields: The impact of the gender stereotype of math anchoring phenomenon to talk about vector motion, forces, and science on secondary students’ career aspirations,” Front. and collisions with package drops. I started with a video about Educ. 4 (2019). drone delivery in the United States, but after showing it at one 5. Y. Xie, M. Fang, and K. Shauman, “STEM education,” Annu. class period, a student asked if I had ever heard about Zipline Rev. Sociol. 41, 331 (2015). drones, which deliver medical supplies in Rwanda. And for the 6. C. Riegle-Crumb, B. King, E. Grodsky, and C. Muller, “The remaining classes, this was the video I used to guide student more things change, the more they stay the same? Prior thinking. The importance of the problem was evident and achievement fails to explain gender inequality in entry into students saw connections to benefiting society. It was clear STEM college majors over time,” Am. Educ. Res. J. 49 (6), 1048 they could make a difference; it’s a way physics could make a (2012). difference. Students were able to bring their own questions and ideas to the conversation and all were valued. If students 7. C. McCallum, “Giving back to the community: How African chose to bring up unethical uses of drones and their impacts Americans envision utilizing their PhD,” J. Negro. Educ. 86 (2), on societies, this would be an opportunity to discuss import- 138 (2017). ant matters and how science is not done in a vacuum. 8. J. Smith, A. Metz, and M. Huntoon, “Giving back or giving up: As the units have developed, so have the contributions Native American student experiences in science and engineer- from students. Students approach problems in unique ways ing,” Cultur. Divers. Ethnic Minor. Psychol. 20 (3), 413 (2014). and are able to formulate questions that lead them to an un- derstanding of every objective I have sought to meet. This 9. P. Vincent-Ruz and C. D. Schunn, “The nature of science iden- power of voice was most evident in my most recent unit tity and its role as the driver of student choices,” Int. J. STEM where, after a silence in questions, I told a student that I no- Educ. 5, 48 (2018). ticed there was a Post-it on the desk. The student said, “I am not sure that this is a good question.” My heart sank; I wanted 10. College Board, Student score distributions, AP exams (May this student to see value in their ideas and feel safe to put 2021). 11. National Research Council, A Framework for K-12 Science Ed- ucation: Practices, Crosscutting Concepts, and Core Ideas (The National Academies Press, Washington, DC, 2012), https://doi. org/10.17226/13165. forward new wonderings. After the question was read aloud, 12. B. Reiser, M. Novak, T. McGill, and W. Penuel, “Storyline units: five more students came up to the board with their own sim- An instructional model to support coherence from the stu- ilar questions. The student’s idea was immediately validated dents’ perspective,” J. Sci. Teach. Educ. 32 (7), 805 (2021). and our class grew because of it. Students then came up with 13. Next Generation Science Storylines, “What are storylines?” overarching questions for each group of questions as a class. https://www.nextgenstorylines.org/what-are-storylines (Dec. Students connected with the content and each other. 2021). 14. O. Lee, “Making everyday phenomena phenomenal,” Sci. Child. Bang and Marin noted that the language and discourse so 58 (1), 56 (2020). pnroenv-adloenmtiinnatnhtegsruobujpe.c2t0cSatnudpeonstesbwahrroieidrseinntilfeyaarns imngemtobtehres 15. Teacher Handbook for NextGen Science Storylines, https:// of underrepresented groups state the opportunity to give docs.google.com/document/d/1EnR8AoXSvLJ4r-jlWNms5T back to the community and participate in causes that em- 3ti_AWtWzUtBggIHjmEtE/edit#heading=h.egt1mrl5dpyu . SpThaEsMizefiseoldcisa.7l,i8m,21p,2r2ovDermiveinntgisquonesetioofnthbeoraeradssoannsdfostrolreyalviinneg 16. A. Weizman, Y. Schwartz, and D. Fortus, “The Driving Ques- approaches allowed my students to build relevance in the con- tion Board,” Sci. Teach. 75 (8), 33 (2008). tent with me and to talk about science in their own terms. 17. B. Brown, Science in the City: Culturally Relevant STEM Educa- tion (Harvard Education Press, 2019). I love the questions and the puzzles of physics. I like to fig- 18. P. Bell, D. Morrison, and A. Debarger, Practice Brief 31: How to ure things out and put pieces together. It’s one of the reasons launch STEM investigations that build on student and communi- I love physics and it’s one of the reasons I love teaching. What ty interests and expertise (STEM Teaching Tools, Nov. 2015). would happen if instead of weeding students out of physics, 19. Special thanks to my collaborators in the University of Kan- we rooted our teaching in their realities? What if we, as in- sas /Kansas State Department of Education Physics Advisory structors, were able to let go of the wheel and let our students Group—Brock Baxter, Nicholas Anderson, Meg Richard, drive their investigations into phenomena? These are good Christine Audo, and Kathy Porre. qouutesttoigoentsh,egro. o23d problems, and topics definitely worth figuring 20. M. Bang and A. Marin, “Nature-culture constructs in science learning: Human/non-human agency and intentionality,” J. Res. Sci. Teach. 52, 530 (2015). 21. E. Seymour and N. M. Hewitt, Talking About Leaving: Why Un- References dergraduates Leave the Sciences (Westview Press, Boulder, CO, 1997). 1. C. Riegle-Crumb, B. King, and Y. Irizarry, “Does STEM stand out? Examining racial/ethnic gaps in persistence across postsec- 22. D. A. Guiffrida, “African American student organizations ondary fields,” Educ. Res. 48 (3), 133 (2019). as agents of social integration,” J. Coll. Stud. Dev. 44 (3), 304 2. X. Chen, Students Who Study Science, Technology, Engineering, (2003). 23. Additional Resources: and Mathematics (STEM) in Postsecondary Education (NCES NGSS / AP crosswalk (https://www.nextgenscience.org/ No. 2009-161) (National Center for Education Statistics, In- ngss-accelerated-pathways) stitute of Education Sciences, U.S. Department of Education, NGSS bundles (https://www.nextgenscience.org/resources/ Washington, DC, 2009). bundling-ngss). 3. H. Garrison, “Underrepresentation by race–ethnicity across stages of U.S. science and engineering education,” CBE Life Sci. Educ. 12 (3), 357 (2013). THE PHYSICS TEACHER ◆ Vol. 60, April 2022 317

Physics Challenge for Boris Korsunsky, Column Editor Teachers and Students Weston High School, Weston, MA 02493 [email protected] w Surfing the net Randall J. Scalise (Southern Methodist University, Dallas, TX) 1 2 Jason L. Smith (Richland Community College, 34 Decatur, IL) Jacqueline Wang, student (Hotchkiss School, Lakeville, CT) An infinite net is made of identical wires. The resistance be- Guidelines for contributors tween points 1 and 2 is r, and the resistance between points 1 – We ask that all solutions, preferably in Word format, and 3 is R. Find the resistance R14 between points 1 and 4. be submitted to the dedicated email address We received many solutions to our January Challenge, Lore [email protected]. Each message will receive an of the rings. We are pleased to recognize the following suc- automatic acknowledgment. cessful solvers: – If your name is—for instance—Roger Penrose, Salvatore Basile (Università degli Studi di Palermo, Palermo, please name the file “Penrose22April” (do not include your first initial) when submitting the April Italy) 2022 solution. Philip Blanco (Grossmont College, El Cajon, CA) – The subject line of each message should be the same Phil Cahill (The SI Organization, Inc., Rosemont, PA) as the name of the solution file. Don Easton (Lacombe, Alberta, Canada) – The deadline for submitting the solutions is the last Arunangshu Karmakar, student (Salt Lake School, Kolkata, day of the corresponding month. – Each month, a representative selection of the suc- India) cessful solvers’ names will be published in print and Stephen McAndrew (Sydney, Australia) on the web. Matthew W. Milligan (Farragut High School, Knoxville, TN) – If you have a message for the Column Editor, you Daniel Mixson (Naval Academy Preparatory School, may contact him at [email protected]; however, please do not send your solutions to this Newport, RI) address. Steven Morris (emeritus, Los Angeles Harbor College, Many thanks to all contributors and we hope to Wilmington, CA) hear from many more of you in the future! Carl E. Mungan (U. S. Naval Academy, Annapolis, MD) Pascal Renault (John Tyler Community College, Midlothian, Note: we always welcome and appreciate reader- contributed original Challenges! VA) The solutions to the past Challenges can be found here: https://aapt.scitation.org/topic/collections/ physics-challenge Please note that AAPT member- ship may be required to view the files. Boris Korsunsky, Column Editor 318 THE PHYSICS TEACHER ◆ Vol. 60, April 2022 DOI: 10.1119/10.0010006

Dan MacIsaac, Column Editor, Physics Department, websights SUNY-Buffalo State College, Buffalo, NY 14222; [email protected] WebSights features announcements and reviews of select sites of interest to physics teachers. All sites are copyrighted by their authors. This column is available as a web page at PhysicsEd. BuffaloState.Edu/pubs/WebSights/. If you have successfully used a physics website that you feel is outstanding and appropriate for WebSights, please email me the URL and describe how you use it to teach or learn physics—[email protected]. w Darek Dewey’s Twitter physics videos ples: The modern day “Leaning Tower of Piza” that is San Francisco’s friction pile supported Millennium Tower: A 56- https://twitter.com/DarekDewey/ story luxury condominium building tilting and turning, and @DarekDewey the quite infamous deadly collapse of the Champlain Towers South condominium, built on subsiding surfside Miami Dewey is a physics teacher at St. Michael-Albertville (MN) Beach waterfront property. Both are complex situations, with H.S. and his frequent (near daily) delightful tweets usually analyses that have partial roots in the conceptual errors relat- show some interesting bit of physics via short (usually ing to soil properties and building foundations. Josh Porter’s < 1 min) video tweets of sometimes classic, sometimes high- “Building Integrity” YouTube channel has multiple strong ly imaginative staged physics demonstrations, particularly videos about the physics, engineering design failures, and optics and mechanics demos, often with imaginative Rube economic and legal decisions and analyses of both structures. Goldberg-esque twists. Recent videos include an analyzable The discussion of the SF friction pile performance and the reverse ballistic pendulum, laser paths in a cardboard box possible initiation of the surfside collapse by punching shear lined with mirrors, regelation of ice, spectra from prisms, a with a possible nighttime thermal stress cycle final trigger rolling lug nut wrench raising and lowering a mass as it rolls are two particularly good videos. Finally, Grady Hillhouse’s up and down two steel lab clamp bars, collisions of carts, “Practical Engineering” channel also has great videos about including (heavily) modified Atwood’s machine-like arrange- The SF and Miami Beach failures (and much more). ments with various pulleys, resonance demonstrations, var- (And the tallest building in SF is for sale cheap, if you are ious Hot Wheels car demos, a Newton’s cradle with charged seeking an exceptionally poor real estate investment.) balloons, tilted track friction demos, wave diffractions, ball bearing in glycerin, polarizing filters, etc. Many of the vid- Submitted by Kathleen Falconer of uni-Köln Physikdidaktik eos are of traditional old chestnuts but still lots of fun new insights and challenges to ponder (I enjoyed the two balls, DOI: 10.1119/10.0010008 one rolling and the other bouncing down the ramp tracking vertical positions). A delightful daily video delivery from w Gregg Swackhamer’s HS Honors Physics website Darek. He and Frank Noschese are worth getting a Twitter account for, and they follow a significant community of phys- swackhamer.weebly.com ics educators using Twitter. The modeling physics community has been fêting the honors Recommended by Frank Noschese @fnoschese physics website of Swackhamer, a founding ASU modeling physics developer. Jane Jackson of ASU Physics writes: DOI: 10.1119/10.0010007 “He goes deeply and broadly into scientific models. Each w Real-world civil engineering events for introduc- chapter of his two courses focuses on a model (or two). In tory mechanics: The Citicorp Center, Millenium each chapter: Tower (SF), and Champlain Towers South structures – He lists system members, system properties, system inter- tinyurl.com/WS-CiticorpNYC1 actions. tinyurl.com/WS-CiticorpNYC2 tinyurl.com/WS-CiticorpNYC3 – He lists things that each model can explain. tinyurl.com/WS-SFMillenniumT1 en.wikipedia.org/wiki/Millennium_Tower_(San_Francisco) – He includes GLOWSCRIPT animations and simulations en.wikipedia.org/wiki/Surfside_condominium_collapse that he developed. youtube.com/c/BuildingIntegrity tinyurl.com/ws-PE-SF1 And much more! (Objectives, practice tests, videos and rep- resentations by physicists, discussions of concepts, connect- I regularly include real-world engineering examples when ing ideas for content coherence) teaching Newton’s laws and then statics in introductory phys- In Physics II, click on ‘chapter 14’. It's a many-particle model ics, particularly the example of the structural design flaw in for condensed matter. Read his discussion ‘What is a field?’ the Midtown NYC Citicorp Center skyscraper caught by an on that webpage. Wow! Coherent. Excellent! (David Hestenes undergraduate engineering student. A positive tale of how agrees.) things were caught and fixed before failure. (Chapter 13 is on temperature and kinetic theory; these two Kathleen Falconer reports she uses two more recent exam- chapters would fit into a chemistry course, too. Chapter 15 is thermodynamics.)” DOI: 10.1119/10.0010009 THE PHYSICS TEACHER ◆ Vol. 59, April 2021 319