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Whatroledoesstaticfrictionforceplayforarollingobject?HowcanIknowwhatdirectionitpoints?
Fundamentally,whatdoesafrictionforcedoforarollingobject?Iamveryconfusedbythewaymytextbookexplainsit.Inmytextbook,itsays:
Awheelrollingonahorizontalflatsurfaceataconstantvelocityexperiencesnofrictionforce.Why?
Onthesamesurface,thereisanaccelerationofthewheelpointingtotheright(probablycausedbyaforce),sotheballisangularlyacceleratingintheclockwisedirection.Inthiscase,africtionforceappears,anditisalsopointingtotheright.Howcome?Whatdoesthefrictiondoforthiswheel?
Onaninclinedplane,aballfreelyrollsdownthesurface.Thedirectionoffrictionisuptheramp,whichconfusesmebecauseinthepreviousexamplethefrictionforcewasinthedirectionofthewheel'sacceleration.
Andthereisadifferenceifawheelisfreelyrollingandifthereisatorqueactingontheball'scenterofmass.WHY???
Whatdoesfrictiondointhesecases?Howdoesitcauseanobjecttoroll?
forces friction
askedJan11at18:37RichardSong6 1
Staticfriction,asitactsinrollingwithoutslipping. RichardSong
Jan11at18:41
Andstaticfrictionsupposedlypreventsthewheelfromsliding,right?
RichardSong Jan11at18:46
ThenhowdoIknowwhichwaysomethingwouldslide?HowdoIknowwhichwayawheelWOULDslide?RichardSong
Jan11at18:58
Related:physics.stackexchange.com/questions/7657/ dmckee
Jan11at22:25
2Answers
Hopefullythiswillansweratleastsomeofyourquestions.Ifyouconsideraballintiallyatrestonafrictionlesssurface,ifaforceisexertedthroughthecentreofmassoftheballitwillslideacrossthesurfacewithnorotation,therewillonlybetranslationalmotion.
Ifyouconsiderthecasewherethereisfriction,iftheforceisagainappliedtoastationaryballthefrictionalforcewillactintheoppositedirectiontotheforcebut
thatrestsontheground.Thisfrictionappliesatorquetotheballwhichstartstherotation.Sostaticfrictionisinfactnecessaryforaballtobeginrolling.
attheedgeoftheball
Theconditionforrollingatspeed
isthattheangularvelocityoftheballisgivenby
fromthisthetopoftheballwillmoveatspeed
thecentreofmassoftheballwillmoveat
andthebottomedgeoftheballwillinstantaneouslybeatrest.Soastheedgetouchingthegroundisstationaryitexperiencesnofriction.
2
2 [.
2 2
Sofrictionisnecessaryforaballtostartrollingbutoncetherollingconditionhasbeenmettheballexperiencesnofriction.
answeredJan11at19:03Chris2807770 1 1 16
Thankyouforyourexplanations.Ihaveconcludedthefollowing:pleasecorrectmeifIamwrong.RichardSong
Jan11at19:59
Ifaballhasaforceactingthroughitscenterofmass(andthereforenotorqueisgeneratedbythatforce),withnofrictionitwilljustslideforward.Iftheforceactedtowardstheright,thentherewouldbeafrictionforceactingtowardstheleft,thusgeneratingatorqueaboutthecenterofmass.
RichardSong Jan11at20:02
InregardtoChris2807'sanswer,Ihaveaquestion:Ifaballisrollingdownthehillonitsown,thereisacontinualcomponentofgravitationalforcethatpullsitdowntheincline.Sincethisforceproducesnotorqueaboutthecenterofmass,Ihaveconcludedthatafrictionalforcemustbeexertedonthecontactpointatalltimeswhentheballslidesdowntheincline,orelseitwouldslide.Whatdoyoumeanbythefactthatoncetherollingconditionismettheballexperiencesnofriction?
RichardSong Jan11at20:17
1
Nice.Youcanalsotaketheoppositeapproach:considerwhathappensifanexternalcouple(puretorque)is
suppliedaroundahorizontalaxis.Withoutfrictiontheballspinsinplace,butwithfrictiontheballappliesaforcetothegroundandthereactionforcebothcancelsmuchoftheappliedcoupleandcausestheballtobegintranslationalmotion.
dmckee Jan11at22:23
@dmckee+1forthatcomment,prettycooleffect.Acoolexampleofthisisprofessionaltenpinbowlers,theyproducelotsofsidespinontheballwhichhasnoeffect(astheboardsareverypolishedandhavelittlefrictionwiththeball)untilthelastfewfeetwheretheyarelesswellpolishedandtheballmoveslaterally.Havealookatthisyoutube.com/watch?v=NiBXo2KjdBA
Chris2807 Jan11at23:06
1.
Ifthewheelisrollingatconstantvelocitywithoutanyotherforcesacting,thenthereisnotendencyforslippagebetweenthewheelandthesurface,sothereisnofriction.Frictionwillonlyacttotrytopreventslippagebetween2surfaces.
2.
Presumablyinthiscasethereisatorqueactingontheaxisoftheball/wheel?Thistorquewillacttogiveangularaccelerationtothewheel(clockwise).Iftherewasnofrictionthentheangularvelocitywouldincreaseandtherewouldbeslippagebetweenthewheelandthesurface.However,frictionexistsandwilltrytopreventtheslippage,whichiswhyitactstotheright.Intryingtopreventthisslippage,thefrictionalsoexertsahorizontallinearforceonthewheel,givingitaccelerationtotheright,soitspeedsup.Thisishowacaraccelerateshorizontally,usingfrictionbetweenthewheelsandtheroad.
3.
Ontheinclinedplane,theballwilltendtoslidedownwardsandiftherewasnofrictionthenagaintherewouldbeslippagebetweentheballandtheinclinedsurface.Perhapsthebestwaytothinkaboutitis:"Whichwayisslippagegoingtooccuriftherewasnofriction?"Frictionwillalwaystrytocounteractslippage,sohereitactsuptheslopetotrytopreventtheballslippingdowntheslope.Thishastheeffectofapplyingamomenttotheball,whichwillcauseittostartrolling.
answeredJan11at19:09Time4Tea903 1 16
Sowhatifthereisaforcethatcausesnotorqueandaforcethatcausestorquethatactonawheel.Soforexample,oneforceactsonthecenterofmasswhileanotheractsonthetopofthewheel.Thewheelisonaflatsurface.Doesthewheelneedfrictiontoroll?
RichardSong Jan11at21:29
Fortheforcethroughthecenter,thewheelwillneedfrictiontostartrolling,otherwiseitwilljustslidehorizontally.Fortheforceonthetop,ifthereisnofrictionthenthewheelwillstartbothmovinglaterallyandrotating.Thesubsequentmotionwilldependonhowtheforcebehavesasthewheelturnswhetheritturnswiththewheelorstayspointinghorizontally(Iassumeitactsatthesamepoint).
Time4Tea Jan11at21:56
