For the component described in the problem indicated, determine
(a) The principal mass moments of inertia at the origin,
(b) The principal axes of inertia at the origin. Sketch the body and show the orientation of the principal axes of inertia relative to the x, y, and z axes. Probs. 9.143 and 9.167: The machine element shown is fabricated from steel. Determine the mass moment of inertia of the assembly with respect to (a) the x axis, (b) the y axis, (c) the z axis is. (The specific weight of steel is 0.284 lb/in.3.)

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2 in. 2 in. 1 in. 1 in. 3 in. 2 in.