A uniform 4.00 kg square solid wooden gate 2.00 m on each side hangs vertically

Question

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 1.20 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. 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 1.20 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.

Explanation / Answer

Before collission the toatal angular momentum is L_i = mv( a / 2 )

After the collission the angular momentum is L_f = - m u ( a / 2 ) + I

                                                                              = - m u + 1/ 3 M a^2

            mv( a / 2 ) = - m u + 1/ 3 M a^2

                = 3/2 (m /M a) ( u +v )

                   = 3/2 * ( 4.00kg / 1.20 * 2.00) ( 5.00 - (2.50 ) m/s

                   = 6.24 rad /s

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