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PHY183-Lecture34

# PHY183-Lecture34 - Moment of Inertia for Constant Density...

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March 23, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 34 March 23, 2006 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 ! The mass for constant density ! The moment of inertia I = ! r " 2 dV V # M = ! dV V " = ! V I = M V r ! 2 dV V " March 23, 2006 Physics for Scientists&Engineers 1 3 Moments of Inertia Moments of Inertia ! Solid cylinder ! Hollow cylinder ! Hoop ! 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 23, 2006 Physics for Scientists&Engineers 1 4 Parallel Axes Theorem Parallel Axes Theorem ! How to find moment of inertia if axis of rotation does not go through the center of mass ! If z’ is the rotation axis, let axis z be a parallel axis through the center of mass ! We know moment of inertia around z!

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March 23, 2006 Physics for Scientists&Engineers 1 5 Parallel Axes Theorem (2) ! Relationship between old and new coordinates !
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