A uniform 4.00 kg square solid wooden gate 2.00 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.30 kg raven flying horizontally at 5.00 m\s flies into this door at its center and bounces back at 2.50 m/s in the opposite direction. What is the angular speed of the gate just after it is struck by the unfortunate raven?