# Problem: A thin, uniform rod is bent into a square of side length a. If the total mass is M, find the moment of inertia about an axis through the center and perpendicular to the plane of the square. (Hint: Use the parallel-axis theorem.)

###### FREE Expert Solution

We are required to derive the expression of the moment of inertia of the square.

Moment of inertia of a thin rod about its center and perpendicular to the length:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{12}}{\mathbf{M}}{{\mathbf{L}}}^{{\mathbf{2}}}}$

Parallel axis theorem:

$\overline{){\mathbf{I}}{\mathbf{=}}{{\mathbf{I}}}_{\mathbf{c}\mathbf{m}}{\mathbf{+}}{\mathbf{m}}{{\mathbf{d}}}^{{\mathbf{2}}}}$ d is the distance from the center of mass to the parallel axis.

87% (379 ratings) ###### Problem Details

A thin, uniform rod is bent into a square of side length a. If the total mass is M, find the moment of inertia about an axis through the center and perpendicular to the plane of the square. (Hint: Use the parallel-axis theorem.)