mass_moments

# mass_moments - square root of the mass moment of inertia...

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Mass Moments of Inertia a) Definition: For a rigid body moving within the x-y plane (rotations about the z- axis), the mass moment of inertia about the z-axis passing through point A is defined as: I zz ( ) A = x 2 + y 2 ( ) dm b) Parallel axis theorem: If the mass moment of inertia is known for the centroid G of a rigid body, then the mass moment of inertia about another point A is given by: I zz ( ) A = I zz ( ) G + m d 2 where m is the mass of the body and d is the distance between points A and G. c) Radius of gyration: The radius of gyration of a rigid body is defined as the
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Unformatted text preview: square root of the mass moment of inertia divided by the mass of the body: k A = I zz ( ) A m d) Centroidal mass moments of inertia for some common shapes of bodies: i. Homogeneous cylinder of radius R and mass m: I zz ( ) G = 1 2 m R 2 ii. Thin homogeneous bar of length L and mass m: I zz ( ) G = 1 12 m L 2 iii. Homogeneous rectangular plate of mass m and dimensions a x b: I zz ( ) G = 1 12 m a 2 + b 2 ( ) iv. Homogeneous sphere of radius R and mass m: I zz ( ) G = 2 5 m R 2 A x y dm...
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