W9.4 - March 10, 2008 Physics for Scientists&Engineers...

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Unformatted text preview: March 10, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Lecture 34 March 10, 2008 Physics for Scientists&Engineers 1 2 Moment of Inertia for Constant Density Moment of Inertia for Constant Density If we take our results for the moment of inertia and assume that the density is constant we get • The moment of inertia for constant density ρ • The mass for constant density ρ • The moment of inertia I = ! r " 2 dV V # M = ! dV V " = ! V I = M V r ! 2 dV V March 10, 2008 Physics for Scientists&Engineers 1 2 Moment of Inertia for Constant Density Moment of Inertia for Constant Density If we take our results for the moment of inertia and assume that the density is constant we get • The moment of inertia for constant density ρ • The mass for constant density ρ • The moment of inertia I = ! r " 2 dV V # M = ! dV V " = ! V I = M V r ! 2 dV V " March 10, 2008 Physics for Scientists&Engineers 1 3 Moments of Inertia Moments of Inertia Solid cylinder Hoop Hollow cylinder Rod Solid sphere Hollow sphere Rectangular block Question : what is the common form? I = 1 2 MR 2 I = MR 2 I = 1 2 M R 1 2 + R 2 2 ( ) I = 1 12 Mh 2 I = 2 5 MR 2 I = 2 3 MR 2 I = 1 12 M ( a 2 + b 2 ) I = cMR 2 with c ! (0,1] March 10, 2008 Physics for Scientists&Engineers 1 4 Parallel Axes Theorem Parallel Axes Theorem Now that we have solved the problem of the moment of inertia of a body rotating on an axis through the center of mass, let’s get the moment of inertia for bodies...
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This note was uploaded on 04/06/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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W9.4 - March 10, 2008 Physics for Scientists&Engineers...

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