Calculating Moment of Inertia for a Rigid Body

[ehrenfest]

Homework Statement

A rigid body consists of three thin uniform rods, each of mass m and length 2a, held mutually perpendicular at their midpoints. Show that the moment of inertia is the same for any axis passing through the origin.

Homework Equations

The Attempt at a Solution

I calculated the principal moments of inertia. To show this, do I need to find a coordinate transformation to take one of the principal axes to an arbitrary axis that goes through the origin and then show that the transformation does not change that element on the diagonal of the inertia tensor? Or is there another way to do this?

 

[ehrenfest]

anyone?

 

[ehrenfest]

please?

 

[pam]

The three principal moments of inertia are equal.
This means the tensor of inertia is proportional to the unit matrix,
so any rotation will not change the tensor of inertia.
It will still be the unit matrix in any rotated system.