A homogeneous cube, each edge of which has a length l, is initially in a position of unstable equilibrium with one edge in contact with a horizontal plane. The cube is then given a small displacement and allowed to fall. Show that the angular velocity of the cube when one face strikes the plane is given by
ω2=Alg(2−1)
where A=3/2 if the edge cannot slide on the plane and where A=12/5 if sliding can occur without friction.