理论力学第十一章英文ppt课件.ppt

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1、§12.4TheoremofmotionofthecenterofmassChapter12:TheoremofMomentum§12.1Thecenterofmassofasystemofparticles§12.2Momentumandimpulse§12.3TheoremofmomentumThecenterofmass.Thecenterofmassofasystemofparticlesiscalledcenterofmass.Itisanimportantconceptrepresentingthedistributionofmassinanysystem

2、ofparticles.Thepositionofthecenterofmasscis§12.1TheCenterofMassofaSystemofParticlesExternalforcesaretheforcesexertedonthemembersofasystembyparticlesorbodiesnotbelongingtothegivensystemInternalforcesaretheforcesofinteractionbetweenthemembersofthesamesystem.Asfarasthewholesystemofparticle

3、sisconcerned,thegeometricalsum(theprincipalvector)ofalltheinternalforcesofasystemiszero.Thesumofthemoments(theprincipalmoment)ofalltheinternalforcesofasystemwithrespecttoanycenterofaxisiszero,too.2.Externalforcesandinternalforcesofasystemofparticles1)Momentumofaparticle.Theproductofthem

4、assofaparticleanditsvelocityiscalledthemomentumofaparticle.Itisatime-dependentvectorwiththesamedirectionasthevelocity,theunitofwhichiskgm/s.Momentumisaphysicalquantitymeasuringtheintensityofthemechanicalmotionofamaterialbody.Forexample,thevelocityofabulletisbigbutitsmassissmall.Intheca

5、seofaboatitisjustopposite.§12.2MomentumandImpulse1.Momentum2)Themomentumofasystemofparticlesisdefinedasthevectorequaltothegeometricsumofthemomentaofalltheparticlesofthesystem:Themomentumofasystemisequaltotheproductofthemassofthewholesystemandthevelocityofitscenterofmass..3)Momentumofasy

6、stemofrigidbodies:Assumethatthemassandthevelocityofthecenterofmassofthei-thrigidbodyare.Forthewholesystemwegetthen..,,,.,IntermsofprojectionsoncartesianaxeswehaveInthemechanismshowninthefigure,OArotatewithaconstantangularvelocityw.AssumethatOA=L,OB=L.TherodsOAandABarehomogeneousandofmas

7、sm.ThemassoftheslideblockatBisalsom.Determinethemomentumofthesystemwhenj=45º.ExampleFortherodOAmass=.Fortheslideblockmass=.FortherodAB:mass=Solution:2)Forceisavariablevector(Includemagnitudeanddirection.)TheelementaryimpulseisTheimpulseis1)Forceisaconstantvector.2.Impulse:Thepr