# Proof: Principal Moment of Inertia

1. Nov 6, 2006

### knightpraetor

How do i go about proving that none of the principal moments of inertia can exceed the sum of the other two?

Someone suggested the triangle inequality, but i don't understand how to use it.

2. Nov 6, 2006

### Galileo

Just write out the definitions:

$$I_x=\int (y^2+z^2)dm$$
$$I_y=\int (x^2+z^2)dm$$
$$I_z=\int (x^2+y^2)dm$$

and fiddle around with that.