Given an arbitrary body and three rectangular axes x, y,

Chapter 9, Problem 9.176

(choose chapter or problem)

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 be 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 \(I_x\le I_y+I_z\) and the two similar inequalities are satisfied. Further, prove that \(I_{y} \geq \frac{1}{2} I_{x}\) if the body is a homogeneous solid of revolution, where x is the axis of revolution and y is a transverse axis.