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 w0 the angular velocity of the crate immediately before B strikes the floor, determine (a) the angular velocity of the crate immediately after B strikes the floor, (b) the fraction of the kinetic energy of the crate lost during the impact, (c) the angle theta through which the crate will rotate after B strikes the floor.