Lec16_Angular_Momentum

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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