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lec15 - Physics I Class 15 Conservation of Angular Momentum...

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15-1 Physics I Class 15 Conservation of Angular Momentum Rev. 09-Oct-04 GB
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15-2 Angular Momentum of a Particle Review v m p = r center of rotation (defined) Angular momentum of a particle once a center is defined: p r × = l (What is the direction of angular momentum here?) Once we define a center (or axis) of rotation, any object with a linear momentum that does not move directly through that point has an angular momentum defined relative to the chosen center.
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15-3 Angular Momentum of a Particle Angular Momentum of an Object For a solid object, each atom has its own angular momentum: ) v m ( r p r i i i i i i × = × = l The direction is the same as the direction of angular velocity. The magnitude is 2 i i i i i i i i i i i r m r r m | v | | r | m ) sin( | p | | r | | | ϖ = ϖ = = θ = l so 2 i i i r m ϖ = l The total angular momentum, summing all atoms, is ϖ = ϖ = = I r m L 2 i i i l
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15-4 How Does Angular Momentum of a Particle Change with Time? Take the time derivative of angular momentum: t d p d r p t d r d ) p r ( t d d t d d × + × = × = l
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