Angular MomentumInertia and VelocityMoment of MomentumApplying TorqueSpinning MassAngular Momentum ConservedInternal Angular MomentumInternal MovementConservationAngular MomentumAngular MomentumInertia and VelocityInertia and VelocityIn the law of action we began with mass and In the law of action we began with mass and accelerationacceleration•F = maF = maThis was generalized to use momentum: This was generalized to use momentum: p = mvp = mv..tpFMoment of Momentum Moment of Momentum To continue the analysis of To continue the analysis of rotational motion, we must rotational motion, we must also extend the idea of also extend the idea of momentum.momentum.rpsinrpL Applying TorqueApplying TorqueAn external torque changes angular momentum.An external torque changes angular momentum.LL+rpsinptLSpinning MassSpinning MassThe moment of inertia is the analog of mass for The moment of inertia is the analog of mass for rotational motion.rotational motion.The analog for angular momentum would be:The analog for angular momentum would be:IL Angular Momentum Angular Momentum ConservedConservedWith no net external torque, angular momentum is With no net external torque, angular momentum is constant.constant.•The angular momentum of an isolated system is conservedThe angular momentum of an isolated system is conservedconstant0LtLInternal Angular Internal Angular MomentumMomentumA system may have more than A system may have more than one rotating axis.one rotating axis.The total angular momentum is The total angular momentum is the sum of separate vectors.the sum of separate vectors.•LLtotaltotal = = LLss + + LLww = = LLwwLwLs = 0Internal MovementInternal MovementInternal torques cancel out.Internal torques cancel out.Conservation requires that Conservation requires that the sum stay constant.the sum stay constant.•LLtotaltotal = = LLss + (- + (-LLww) = ) = LLww•LLss = 2 = 2LLww-LwLs = 2 LwConservationConservationWith no external torque, angular momentum is With no external torque, angular momentum is constant.constant.• LL//tt = 0= 0• LL = constant = constantrI = mr2mr/2I =
View Full Document
Unlocking...