# Parallel Axis Theorem

Hi all, I have run into a problem requiring the use of the parallel axis theorem. I'm kind of lost as to where to start. Can anyone help?

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. Use the parallel-axis theorem.

TIA.

Doc Al
Mentor
Treat the object as a set of four thin rods. I assume you know how to find the moment of inertia of each rod about its own center. Now use the parallel axis theorem to find the moment of inertia of each rod about the center of the square.

Alright. So, first of all, you should know that the moment of inertia of a rectangular plate, axis through the center of the plate is:

I = (1/12)*M*(a^2+b^2)

1. Simply, for a square it would just be (a^2+a^2) or (2a^2)
2. Then, we find moment of inertia from the parallel-axis theorem.
3. Finally, take the moment of inertia from the parallel-axis theorem and subtract.
(so, parallel-axis - moment of inertia)
4. That's it, that should be the answer.