Problems (Rotational Dynamics) Answers

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1、SJPOTrainingMechanicsProblemSetRotationalDynamicsTanJingLongLeeBingQianMay24,20141GeneralRound1.1CentripetalForce1.Aparticlemovesataconstantspeedinacircularpathwitharadiusof2:06cm.Iftheparticlemakesfourrevolutionseachsecond,whatisthemagnitudeofitsacceleration?Solution:1

2、3m/s2.AcarnivalFerriswheelhasa15mradiusandcompletesveturnsaboutitshorizontalaxiseveryminute.Whatistheacclerationofthepassengerathislowestpointduringtheride?Solution:4:1m/s2,takingupwardsaspositive.3.Atetherballisona2:1mstringwhichmakesanangleof22withtheverticalasitmov

3、esaroundthepoleinahorizontalplane.Ifthemassoftheballis1:3kg,whatistheball'sspeed?Solution:1:8m/s,takingupwardsaspositive.4.Atractormovingforwardatuniformspeedonhorizontalgroundhasafrontwheeldiameterof0:8mandbackwheeldiameterof1:25m.Thehorizontaldistancebetweentheaxlesof

4、thetwowheelsis2m.Duringatripapebblestucktothefrontwheel ewothewheelatthehighestpoint.0:2slater,anotherpebble ewothebackwheelatitshighestpointtoo.Thetwopebbleslandedonthesamespotontheground.Findthespeedofthetractor.Solution:5m/s11.2Position-dependentQuantities1.Alarges

5、poolofropeliesontheground,asshowninthediagrambelow.Theend,labeledX,ispulledadistanceSinthehorizontaldirection.Thespoolrollswithoutslipping.IntermsofS,determinethedistancethespool'scenterofmassmoves.XSolution:S=22.PQRSisalight,rigidrodwithmassesattachedtoitasshowninthedi

6、agram,wherePQ=QR=RS=l.DeterminethemomentofinertiaofthesystemaboutXY.XPQRSYSolution:50ml23.TwoidenticalrectangularbricksoflengthSarepiledwithoneontopoftheotheronatable.WhatisthamaximumdistanceL(seethegurebelow)thatthetopbrickcanbeextendedbeyongtheedgeofthetableforthesys

7、temtoremainbalanced?(Notethatthegureisnotdrawntoscale.)Solution:3S4Page24.Adiatomicmoleculeconsistsoftwopointmasses,m1andm2,separatedbyadistancer.Ifxisthedistancefromm1tothecenterofmass,whatisthemomentofinertiaaboutanaxisparalleltothemolecularaxisandpassesthroughthecen

8、terofmass.Notethatthemolecularaxisisthelinejoiningthetwoatomsinthediatomicsmolecule.Solution:05.Inthegurebelo