A uniform square crate is released from rest with corner D directly above A and it rotates about A until its corner B impacts the floor and then it rotates about B. The floor is rough enough to prevent slipping and the corner at B does not rebound on impact. Determine, (a) as a function of g and `, the angular velocity of the crate !E2 just before impact. (b) as a function of !E2, the angular velocity of the crate immediately after impact !E3. (c) the fraction of energy lost during the impact. (d) the maximum achieved after the impact. During the impact, assume that the weight force is non-impulsive.