A uniformly loaded square crate is released from rest with its corner D directly above A; it rotates about A until its corner B strikes the floor, and then rotates about B. The floor is sufficiently rough to prevent slipping and the impact at B is perfectly plastic. Denoting by ?0 the angular velocity of the crate immediately after B strikes the floor, determine

(a) The angular velocity of the crate immediately before B strikes the floor,

(b) The fraction of the kinetic energy of the crate lost during the impact,

(c) The angle θ through which the crate will rotate after B strikes the floor.