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lecture20

# lecture20 - Rotation of rigid bodies A rigid body is a...

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Rotation of rigid bodies A rigid body is a system where internal forces hold each part in the same relative position 2 2 1 2 , 2 1 , , , CM i CM i i lab CM CM system lab system Mv v m K K K For any system: For rigid body: rot i CM i i K v m 2 , 2 1 i i m M

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Kinetic Energy and Rotation. Moment of Inertia.   2 2 2 1 2 2 1 2 2 1 i i i i i i i i i rot r m r m v m K i i i r m I 2 2 2 1 I K rot 2 2 1 2 2 1 CM CM I Mv K If R v CM (rolling without slipping) and 2 kMR I then ) 1 ( 2 2 1 2 2 2 1 2 2 1 k Mv R v kMR Mv K CM CM CM i i m M dm r I 2 dm M
Note: I=kMR 2 , where k 1

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Example: Two spheres have the same radius and equal masses. One is made of solid aluminum and the other is a hollow shell of gold. Which one has the biggest moment of inertia about an axis through its center?
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lecture20 - Rotation of rigid bodies A rigid body is a...

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