# Homework Help: Angular Velocity Problem

1. Nov 13, 2005

### Euclid

A uniform cube is positioned in unstable equilibrium on one of its edges. It's given a small nudge. Show the angular velocity when one face hits the ground is $$\frac{12g}{5l}(\sqrt{2}-1)$$, when the block slips without friction, where l is the length of its side.
It seems to me the best approach is to use energy conservation:
$$mg\frac{l}{\sqrt{2}}=\frac{1}{2}I_{CM}\omega^2+\frac{1}{2}mv_{CM}^2+mg\frac{l}{2}$$. However, the difficulty seems to arise in finding a relation between v_CM and \omega. Any ideas?