Ch. 12 Q 78 - Why can't I solve this by saying the initial kinetic energy of the bullet is equal to the rotational kinetic energy of the door (plus the bullet, though the bullet's mass is negligible relative to the door, so really its just the door that matters).

78. III A 10g bullet traveling at 400m/s strikes a 10kg,1.0m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door just after impact