Objec&vestestedinExam2

C)Answerques,onsA,Bagain,butnowwithacylinderthatcanroll,withmassM=0.2kgandradiusR=10cm.

Inthefigureshown,a30kgchildstandsontheedgeofasta,onarymerry‐go‐roundofradius2.0m.Therota,onaliner,aofthemerry‐go‐roundaboutitsrota,onaxisis150kg∙m2.Thechildcatchesaballofmass1.0kgthrownbyafriend.Justbeforetheballiscaught,ithasahorizontalvelocityofmagnitude12m/s,atangleφ=37°withalinetangenttotheouteredgeofthemerry‐go‐round,asshown.Whatistheangularspeedofthemerry‐go‐roundjustaUertheballiscaught?

C)Answerques,onsA,Bagain,butnowwitharollingcylinder,withmassM=0.2kgandradiusR=10cm.

Ifitisacylinder,itcannotrollinthefric,onlesspartofthetrack,itslides.Ontheflatsurfacewithfric,on,itwillroll,butitwillnotloseenergy!So,itwillreachthea1mmaximumheightonbothsides,andgobackandforthforever(ideally).

Inthefigureshown,a30kgchildstandsontheedgeofasta,onarymerry‐go‐roundofradius2.0m.Therota,onaliner,aofthemerry‐go‐roundaboutitsrota,onaxisis150kg∙m2.Thechildcatchesaballofmass1.0kgthrownbyafriend.Justbeforetheballiscaught,ithasahorizontalvelocityofmagnitude12m/s,atangleφ=37°withalinetangenttotheouteredgeofthemerry‐go‐round,asshown.Whatistheangularspeedofthemerry‐go‐roundjustaUertheballiscaught?

Thisisa“collision”whereangularmomentumabouttheaxisofthemerry‐go‐roundisconserved.

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L o = r ×m v (into the page)

L0 = Rmv sin(90o + φ) = Rmv cosφL0 = 2.0m ×1.0kg×12m /s× cos(37o) =19.7kgm2 /s

AUerthe“collision”,wehaveasystemwiththreepieces(merry‐go‐round,childandball),allrota,ngabouttheaxis.Thus,wecanwritetheangularmomentumasL=Iω,whereωisangularspeedwewanttofindout.Therota,onaliner,aofthesystemisI=150kg∙m2+30kg(2.0m)2+1.0kg(2.0m)2=274kg∙m2

Theangularmomentumbeforethecollisionisthatofjusttheball:

Sinceangularmomentumisconserved,L0=Iω,andω=L0/I=(19.7kg∙m2/s)/(274kg∙m2)=0.072rad/s.