正文描述:《Lec16_Angular_Momentum》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、PhysicsIClass16AngularMomentumReview:LinearandAngularAnalogsVariableRigidbodyGeneralizationx→θθ=s/rv→ωω=v/rωa→αα=a/rα22m→II=mr→∫dmrF→ττ=rF→rFsinθτ=r×F⊥p→ll=Iω→rpl=r×pAdditionalLinearandAngularAnalogsLinearAngularF=maτ=Iα1212K=mvK=Iω22AngularMomentumofaParticleRotationalanal
2、oganalogoflinearmomentum.•Startwithafreeparticlemovinginacenterofrotation(anypointdefined)straightlinepastanarbitrarypoint.•Placetheoriginofacoordinatesystematthepoint.•Thedirectionoftheangularmomentumindicatesthetypeofrotation(clockwise,counterclockwise,etc.)AngularMomentumConservatio
3、nComparethemotionofafreeparticleattwodifferenttimes.Theangularmomentumalwaysθr1r2pointsoutofthepageandthemagnitudeisconstant:
4、l
5、=
6、r×p
7、=rp111
8、l
9、=
10、r×p
11、=rpsinθ222
12、l
13、=(rsinθ)p=rp221Thereforel=l(AngularMomentumConservation)12AngularMomentumofaFiniteObjectSummingthesegivestheangul
14、armomentumoftherotatingobject.2l=∑l=ω∑mr=Iωiiil=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
显示全部收起
温馨提示:
1. 部分包含数学公式或PPT动画的文件,查看预览时可能会显示错乱或异常,文件下载后无此问题,请放心下载。
2. 本文档由用户上传,版权归属用户,天天文库负责整理代发布。如果您对本文档版权有争议请及时联系客服。
3. 下载前请仔细阅读文档内容,确认文档内容符合您的需求后进行下载,若出现内容与标题不符可向本站投诉处理。
4. 下载文档时可能由于网络波动等原因无法下载或下载错误,付费完成后未能成功下载的用户请联系客服处理。