16 - 2D rigid body rotational kinetics - Moment of inertia

16 - 2D rigid body rotational kinetics - Moment of inertia...

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2D Rigid Body Rotational Kinetics Moment of inertia: I 2 I rdm = integration over the body – Special cases for some uniform rigid bodies: (1) Slender rod (mass = M and length = L ) pivoted at the center : I = ML 2 /12 (2) Slender rod (mass = M and length = L ) pivoted at the end: I = ML 2 /3 (3) Circular disk or cylinder (mass = M and radius = R ) pivoted at the center: I = MR 2 /2 (4) A point mass M of negligible size: I = Mr 2 , r = distance from the pivot to the particle – Parallel-axis theorem: I O = I cm + md 2 , d = distance between the pivot point O and center of mass . Note: For a uniform rigid body, the center of mass (cm) coincides with its geometric center. – Moment of inertia of a composite body (assembly of several parts):
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Unformatted text preview: I = Σ I i Example 1. A 7.5 Kg thin rod and a small 5 Kg sphere are mounted on a 25 Kg disk as shown. The size of the sphere can be ignored and the disk is pivoted at its center. Find the moment of inertia of the assembly. ( Ans : 3.2 Kgm 2 ) O R = 0.4 m 2. Two small spheres A ( m A = 2.5 Kg) and B ( m B = 2 Kg) are attached to a 3 Kg slender rod as shown. The sizes of the spheres are negligible and the 2 m long rod is pivoted at point O . Find the moment of inertia of the assembly. ( Ans : 4 Kgm 2 ) O B A 0.6 m 0.5 m 1.5 m...
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This note was uploaded on 10/17/2009 for the course PHYS 2305 taught by Professor Tschang during the Spring '08 term at Virginia Tech.

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16 - 2D rigid body rotational kinetics - Moment of inertia...

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