lecture 18

# lecture 18 - Lecture 18 Rolling Objects 1 Rolling An object...

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1 Lecture 18 Rolling Objects

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2 An object that is rolling combines translational motion (its center of mass moves) and rotational motion (points in the body rotate around the center of mass). For a rolling object 2 2 cm rot T tot 2 1 2 1 ϖ I mv K K K + = + = If the object rolls without slipping then v cm = R ϖ . Rolling
3 Pure Translation Pure Rotation Rolling

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4 Example: Two objects (a solid disk and a solid sphere) are rolling down a ramp. Both objects start from rest and from the same height. Which object reaches the bottom of the ramp first? h θ The object with the largest linear velocity (v) at the bottom of the ramp will win the race.
5 + = + = + = + + = + + = + = 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 1 2 1 0 0 R I m mgh v v R I m mgh R v I mv I mv mgh K U K U E E f f i i f i ϖ Apply conservation of mechanical energy: Example continued Solving for v:

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6 2 sphere 2 disk 5 2 2 1 mR I mR I = = For the disk: For the sphere:
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## This note was uploaded on 07/04/2011 for the course PHYS 121 taught by Professor Staff during the Spring '11 term at ASU.

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lecture 18 - Lecture 18 Rolling Objects 1 Rolling An object...

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