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Ozobot Bit Classroom Application:Linear and Angular Kinematics

Created by

Richard Born

Associate Professor Emeritus

Northern Illinois University

richb@rborn.org

Topics

Science, Physics

Ages

Grades 10 – 12

Duration 30-45 minutes

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Ozobot Classroom Application:

Linear and Angular Kinematics

By Richard Born

Associate Professor Emeritus

Northern Illinois University

rborn@niu.edu

Introduction

Thestudyofthemotionofanobjectinphysics,withoutregardtotheobject’smassandforcescausingthemotion,isknownaskinematics.InanotherOzobotBitclassroomapplication,VelocityasSlopeofPositionvs.TimeGraphs,thekinematicsofmotiononastraightlineisinvestigated.Inthisclassroomapplication,studentswillcontrastlinearandangularkinematicsofOzobotashemovesincircles.Intheprocessofthisinvestigation,studentswilllearnaboutradiansasameasureofangleandhowtomeasureangularspeedinradianspersecond.Inaddition,studentswillcalculateOzobot’sradialacceleration,alsoknownascentripetalacceleration.

DegreesversusRadiansasaMeasureofAngle

Themeasurementofanglescommonlyusesdegreesthroughthestudyofgeometry.However,inmoststudiesofmathematicsandphysicsbeyondgeometry,angularmeasurementisdescribedinradians.Figure1canbeusedasanaidtounderstandthedifferencebetweendegreesandradians.

Figure1

ConsiderdegreesfirstbyobservingFigure1(a).StartingatpointPandmovingcounter-clockwise,anangleθiscreated.Asθincreases,anangleof90°,aright-angle,iscreated.Continuingtoastraight-angle,anangleof180°iscreated.Onecompletecircleresultsinθ=360°.Oncemorearoundthecirclewouldresultinθ=720°.

NowconsiderradiansbyobservingFigure1(b).Radiansaredefinedonthebasisofaunitcircle,i.e.,acirclewitharadiusof1.Thelengthofthearcwhichθsubtendsistheradianmeasure.Aquarterofacircleisthereforeπ/2radians,ahalfcircleisπradians,three-quartersofacircleis3π/2radians,andafullcircleis2π

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radians.Twofullcircleswouldsubtendanangleof4πradians.Forageneralcircleofradiusr,themagnitudeoftheanglesubtendedbyθwouldthesameastheratioofthearclength,L,dividedbytheradius.Therefore,

θ=L/rorL=rθ.Equation1

Itisseenthatradians,θ,arepurenumberswithoutdimensionssincetheyaretheratiooftwolengths,Landr.

Radiansarecommonlyusedinphysicstodescribeangularmeasurements.Forexample,angularspeedwouldbedescribedinradians/second,orrad/sinshort.Angularaccelerationwouldbedescribedinradianspersecondpersecond,orrad/s2inshort.Sinceradiansarepurenumbers,whendealingwithdimensionalanalysis,theunitsforangularvelocitywouldbes-1andtheunitsforangularaccelerationwouldbes-2.

TheOzoMapforthisClassroomApplication

AsshowninFigure2,theOzoMapforthisclassroomapplicationhasOzobotstartinginthelowerleftcorner.Hethenfollowssixsemicircleslabeled1through6,inthatorder.ThesesixsemicirclesarelaidoutinsuchawaythatOzobotfollowsaspiral.ThereisnoOzoBlocklyprogramrequiredforthisclassroomapplication.Ozobotisstartedatthelocationlabeled“Start”bypressingthestartbuttononce.Ozobotwillthentravelataconstantspeed,i.e.,hisdefaultspeed,ashemovesaroundthespiral.EitherOzobot1.0orOzobotBitcanbeused.Bytakingappropriatemeasurementsdescribedinthenextsectionofthisdocument,studentswillbeablelearnsomeconceptsrelatedtoangularkinematics.NotethatalargercopyoftheOzoMap,suitableforcopyingandusebystudentswithanOzobot,canbefoundonthelastpageofthisdocument.

Figure2

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TheAngularKinematicsExperiment

EachstudentlabgroupneedsoneOzobot1.0orOzobotBit,whichisplacedatthelocationlabeled“start”ontheOzoMap,andfacingthedirectionshownbythearrow.Ozobotisthenstartedbyclickingthestartbuttononce.ThehorizontalgraylineontheOzoMapisusedtoseparatethesemicircles1through6ofdecreasingradii.Beforetakinganyquantitativemeasurements,havethestudentsthinkaboutanddiscussthefollowingthreequestionsbymakingsomequalitativeobservations:

1. DoesOzobotappeartohaveaconstantlinearspeedashetravelsinwardonthespiral?[Yes,hislinearspeedisconstantwithavalueequaltothedefaultspeedofOzobot.]

2. DoesOzobotappeartohaveaconstantangularspeed,sayindegreespersecond,ashetraversesthespiral?[No,hisangularspeedincreasesashetraversesthespiral.Herevolves180°oneachofthesemicircles,butittakeshimlesstimetodoitashegetsclosertothecenterofthespiral.]

3. HowmanyradiansdoesOzobottraverseforeachofthesixsemicircles?[Ozobottraversesπradiansforeachofthesixsemicircles.Thisisagoodtimetodiscussradiansifthestudentsarenotfamiliarwithradiansasameasureofangle.]

NowthatthestudentlabgroupshavecompletedsomequalitativeobservationsofOzobot’smotiononthespiral,theyshouldbereadytocollectsomequantitativedata.Eachgroupwillneedametricrulertomeasureandrecordthediameterofthesixsemicircles.Theyshouldrecordthediametertothenearest0.1cmintheprovideddatatableonthenexttothelastpageofthisdocument.Usingthehorizontalgraylineasaguide,diametersshouldbemeasuredatthecentersofthethickblacklinesthatOzobottraverses.Halfthediameterwillthengivethemtheradius.

StopwatchesshouldalsobeprovidedsothatthelabgroupscanrecordthetimerequiredforOzobottotraveleachofthesixsemicircles.Alternatively,studentscanuseastopwatchappontheircellphones.Ineithercase,itissuggestedthattimesberecordedtothenearest0.01second.Thehorizontalgraylinecanbeusedasthestartingandstoppinglocationforeachofthetimemeasurements.Itishelpfulifthestopwatchcanprovide“lap”times,wherealapisthetimetotraverseeachofthesemicircles.Ifclickingthestopwatchonlydisplaystotaltimesincethestartofsemicircle1,thenlaptimescanbeobtainedbycalculatingdifferencesintimes.ThetableofFigure3isprovidedfortheteacherasanexampleoftypicaldatathatlabgroupsmayobtain.

Semicircle# Diameter(cm)

Radius(cm)

SemicircleTime(s)

AngularSpeed(rad/s)

LinearSpeed(cm/s)

Radial(Centripetal)Acceleration(cm/s2)

1 17.8 8.90 9.68 0.325 2.89 0.94 2 15.3 7.65 8.49 0.370 2.83 1.05 3 12.7 6.35 7.00 0.449 2.85 1.28 4 10.2 5.10 5.88 0.534 2.73 1.46 5 7.6 3.80 4.39 0.716 2.72 1.95 6 5.1 2.55 3.35 0.938 2.39 2.24

Figure3

HerearesamplecalculationsforthedatashowninFigure3forsemicircle#1:

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• Diameter:17.8cm,obtainedbymeasurementswithametricruler.• Radius:Halfthediameter.17.8cm/2=8.90cm.• SemicircleTime:9.68s,obtainedbymeasurementswithastopwatchorstopwatchapp.• AngularSpeed:Inrad/s,sincewehavesemicircles,theangularspeedisπ/semicircletime=π/9.68s=

0.325rad/s.• LinearSpeed:Lengthofsemicirclearc/semicircletime=π·Radius/time=π·8.90cm/9.68s=2.89cm/s.• Radial(Centripetal)Acceleration:Fromphysicsac=v2/r=(2.89cm/s)2/8.90cm=0.94cm/s2.

PreparationfortheLesson

1. Makeacopyofthelasttwopages(datatableandOzoMap)ofthisdocumentforeachlabgroup.2. MakesurethattheOzobotsarefullycharged,calibratedforpaper,havecleanwheels,andthemotorsare

tuned.3. StudentsshouldstarttheirOzobotsbypressingthestartbuttononce,withOzobotatthestartlocationon

theOzoMapandfacingthedirectionshownbythearrow.

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DataTablefortheOzobotAngularKinematicsExperiment

Semicircle# Diameter(cm)

Radius(cm)

SemicircleTime(s)

AngularSpeed(rad/s)

LinearSpeed(cm/s)

Radial(Centripetal)Acceleration(cm/s2)

1

2

3

4

5

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Questions:

1. DothedataintheLinearSpeedcolumnofyourdatatableagreereasonablywellwithyourearlierqualitativeobservationsregardinglinearspeed?Explain.

2. DothedataintheAngularSpeedcolumnofyourdatatableagreereasonablywellwithyourearlierqualitativeobservationsregardingangularspeed?Explain.

3. DoesOzobotappeartobeexperiencinganangularaccelerationasittraversesthespiral?Explain.

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