PROBLEM 9.178 Given an arbitrary body and three rectangular axes x, y, and z, prove that the moment of inertia of the body with respect to any one of the three axes cannot be larger than the sum of the moments of inertia of the body with respect to the other two axes. That is, prove that the inequality xyzIII≤+and the two similar inequalities are satisfied. Further, prove that 12yxII≥if the body is a homogeneous solid of revolution, where xis the axis of revolution and yis a transverse axis.
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