Euclid
Nov13-05, 03:39 PM
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+\fr ac{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?
It seems to me the best approach is to use energy conservation:
mg\frac{l}{\sqrt{2}}=\frac{1}{2}I_{CM}\omega^2+\fr ac{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?