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1、PhysicsIClass16AngularMomentumReview:LinearandAngularAnalogsVariableRigidbodyGeneralizationx→θθ=s/r?v→ωω=v/rω?a→αα=a/rα22m→II=mr→∫dmr???F→ττ=rF→rFsinθτ=r×F⊥???p→ll=Iω→rpl=r×pAdditionalLinearandAngularAnalogsLinearAngular????F=maτ=Iα1212K=mvK=Iω22AngularMomentumofaParticleRotationalanal
2、oganalogoflinearmomentum.?Startwithafreeparticlemovinginacenterofrotation(anypointdefined)straightlinepastanarbitrarypoint.?Placetheoriginofacoordinatesystematthepoint.?Thedirectionoftheangularmomentumindicatesthetypeofrotation(clockwise,counterclockwise,etc.)AngularMomentumConservatio
3、nComparethemotionofafreeparticleattwodifferenttimes.Theangularmomentumalways??θr1r2pointsoutofthepageandthemagnitudeisconstant:???
4、l
5、=
6、r×p
7、=rp111???
8、l
9、=
10、r×p
11、=rpsinθ222?
12、l
13、=(rsinθ)p=rp221??Thereforel=l(AngularMomentumConservation)12AngularMomentumofaFiniteObjectSummingthesegivestheangul
14、armomentumoftherotatingobject.???2?l=∑l=ω∑mr=Iωiii??l=IωNewton’sSecondLawAngularMomentumConservationIftherearenoexternaltorques,theangularmomentumofasystemofparticlesisalsoconservedifweputtheoriginatthecenter-of-mass.Also,forarigidobjectrotatingaboutafixedaxiswithnoexternaltorques,??dl
15、τ==0netdtso,?l=constantAngularMomentuminCollisionsExample1Example2Take-AwayConceptsActivity17ConservationofAngularMomentumGoal:Measureacollisionbetweenobjectsrotatingonanaxisandconfirmconservationofangularmomentum.Apparatus:Rotatingdiskwithmotionsensor,thinmetalring,andLoggerProfileAng
16、ularMomentum.xmblProcedure:Droptheringnearthecenterofrotationaxis.Nottolettheringanddisktouchbeforeyouletgoofthering.Measuretheangularvelocityωofthesystemjustbeforethecollisionandimmediatelyafterthecollision.RepeatfivetimesRotationalinertiaI(disk+spool+shaft)=2.6×10-4kgmRotationalinert
17、iaI(ring)=5.1×10-4kgmMassofthering=0.465ParallelAxisTheoremI=I+Mh2whereMisthebody’stotalmasscm2CorrectiontermI=Icom+MrcenterrOffcenter
