problem09_97

University Physics with Modern Physics with Mastering Physics (11th Edition)

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9.97: Introduce the auxiliary variable L , the length of the cylinder, and consider thin cylindrical shells of thickness dr and radius r ; the cross-sectional area of such a shell is , 2 dr r π and the mass of shell is . 2 2 2 dr Lr α π dr rLρ π dm = = The total mass of the cylinder is then α = α = = R R L π dr r L π dm M 0 3 2 3 2 2 and the moment of inertia is
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Unformatted text preview: . 5 3 5 2 2 2 5 4 2 MR R L π dr r L π dm r I R o = α = α = = ∫ ∫ b) This is less than the moment of inertia if all the mass were concentrated at the edge, as with a thin shell with , 2 MR I = and is greater than that for a uniform cylinder with , 2 2 1 MR I = as expected....
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This document was uploaded on 02/04/2008.

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