A uniform, 4.5-kg, square, solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1-kg raven flying horizontally at 5.0m/s flies into this door at its center and bounces back at 2.0m/s in the opposite direction. (a) What is the angular speed of the gate just after it is struck by the unfortunate raven? (b) During the collision, why is the angular momentum conserved, but not the linear momentum?
The Attempt at a Solution
I think that if there is no external torque, angular momentum should be conserved. Since the weight of the gate is in the same line of the gate, there should not be any contribution to torque and therefore angular momentum should be conserved. But how about the linear momentum? In my opinion, all the force should be balanced so that the gate will not move downward. The should not be any external force, however the answer stated that linear momentum is not conserved, because there is an external force exerted by the pivot. But is the force should still be balanced, even it will be spinning?