Problem

Given an arbitrary body and three rectangular axes x, y and z prove that the mass moment o...

Given an arbitrary body and three rectangular axes x, y and z prove that the mass moment of inertia of the body with respect to any one of the three axes cannot lie larger than the sum of the mass moments of inertia of the body with respect to the other two axes. That is prove that the inequality IxIy + Iz and the two similar inequalities are satisfied. Further, prove that Iy ≥ ½Ix  if the body is a homogeneous solid of revolution, where x is the axis of revolution and y is a transverse axis.

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