Lect17

# Lect17 - PHYS 172 Modern Mechanics Lecture 17 Multiparticle...

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Fall 2011 PHYS 172: Modern Mechanics Lecture 17 – Multiparticle Systems, Moment of Inertia Read 9.3 – 9.5 1

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Rotational Kinetic Energy • Consider a rigid system rotating on an axis • All atoms are rotating at the same l angular speed z ! = 2 " T v = r 2
Moment of Inertia K rot = 1 2 [ m 1 r ! 1 2 + m 2 r ! 2 2 + m 3 r ! 3 2 ] " 2 = 1 2 I 2 3

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Some Moments of Inertia I cylinder = 1 12 ML 2 + 1 4 MR 2 I disk = 1 2 2 I sphere = 2 5 2 4
Rigid Rotation about a Point Not the Center of Mass In General K tot = K trans + K rel First, calculate K trans 5

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What is K trans ? K trans = 1 2 Mv CM 2 = 1 2 M ( ! r CM ) 2 = 1 2 ( Mr CM 2 ) 2 ν CM = ω r CM 6
Rigid Rotation about a Point Not the Center of Mass K tot = K trans + K rel K rel = K rot = 1 2 I CM ! 2 K tot = 1 2 ( Mr CM 2 + I CM ) 2 K trans = 1 2 ( 2 CM ) ω 2 7

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Center of mass demo: hovercrafts d ! P tot dt = ! F net , ext ! P tot = M ! v cm for v << c 8
Point particle system 2 2 1 22 tot trans cm P KM v M == For both, real and point system: Point particle system: d !

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Lect17 - PHYS 172 Modern Mechanics Lecture 17 Multiparticle...

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