Center of MassMotion with Many ParticlesForces on One ParticleForce on a SystemInternal ForcesTotal MassSlide 7Translational MotionCenter of MassCenter of MassMotion with Many ParticlesMotion with Many ParticlesReal objects consist of many Real objects consist of many particles.particles.The particles are bound by The particles are bound by internal forces.internal forces.•The object moves as if it The object moves as if it were a single particlewere a single particleParts of the object may Parts of the object may appear to move appear to move independently.independently.Forces on One ParticleForces on One ParticleThere is a net force on each There is a net force on each particle in an object.particle in an object.This corresponds to the particle’s This corresponds to the particle’s acceleration.acceleration.2222)(dtrmddtrdmamFiiiiiiimiriForce on a SystemForce on a SystemFor N particles in a system For N particles in a system the forces add.the forces add.Some forces are internal and Some forces are internal and some are external to the some are external to the system.system.NiiiNiitotaldtrmdFF1221)(m2m3m4m1Internal ForcesInternal ForcesWithin an object all the Within an object all the forces are in pairs.forces are in pairs.These forces must cancel These forces must cancel out in the sum.out in the sum.NiiiNiextnetNiiiNiintNiexttotaldtrmdFFdtrmdFFF122112211)()(0intFTotal MassTotal MassThe sum of all the individual masses in a system is The sum of all the individual masses in a system is the total mass.the total mass. MrmdtdMFdtrmdMMdtrmdMMFmMNiiinetNiiiNiiinetNii1221221221)(1)(Center of MassCenter of MassThe weighted average of the The weighted average of the positions of the particles is positions of the particles is the the center of masscenter of mass.. MrmrNiiiCM1m2m3m4m1rCMTranslational MotionTranslational MotionThe motion of the center of The motion of the center of mass of a system of particles mass of a system of particles depends on the net external depends on the net external force on the system.force on the
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