# Lect19 - PHYS 172: Modern Mechanics Lecture 19 Angular...

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Fall 2011 PHYS 172: Modern Mechanics Lecture 19 – Angular momentum Read 11.1 – 11.3 1

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Angular momentum r r r Angular momentum ~ p, ~ r 2
Angular momentum r r Angular momentum ~ p, ~ r Magnitude of angular momentum of a particle relative to location A sin AA Lr p r p θ == A ! p ! r A sin A r r = 3

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Cross-product Angular momentum of a particle relative to location A ! L A = ! r A ! ! p A ! p ! r A r ! = r A sin " ! L A = yp z ! zp y ( ) , zp x ! xp z ( ) , xp y ! yp x ( ) ! A ! ! B Cross-product: ! A ! ! B = AB sin ! A ! ! B ! A ! B ! A ! ! B = A y B z " A z B y ( ) , A z B x " A x B z ( ) , A x B y " A y B x ( ) ! See book for more L A = r A p sin 4
Examples ! L A = ! r A ! ! p ! r A ! r A ! p ! p ! L ! L See book for more examples 5

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Multiparticle system tot trans rel KK K =+ tot trans rot vib + Split total kinetic energy: Split angular momentum: ! L A = ! L trans , A + ! L rot ! r cm ! r 1 ! r 2 ! r 3 ! p 1 ! L rot = ! r 1 ! ! p 1 + ! r 2 ! ! p 2 + . ! p 3 ! L A = ! r cm + ! r 1 ( ) ! ! p 1 + ! r cm + ! r 2 ( ) ! ! p 2 + ... ! L A = ! r cm ! ! p 1 + ! p 2 + ... ( ) + ! r 1 ! ! p 1 + ! r 2 ! ! p 2 + ... ( ) ! L A = ! r cm ! ! P tot + ! r 1 ! ! p 1 + ! r 2 ! ! p 2 + ... ( ) Translational and rotational angular momenta: !
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## This note was uploaded on 12/07/2011 for the course PHYS 172 taught by Professor ? during the Fall '08 term at Purdue University.

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Lect19 - PHYS 172: Modern Mechanics Lecture 19 Angular...

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