Answer:
The angular velocity is 
Explanation:
From the question we are told that
The mass of wooden gate is 
The length of side is L = 2 m
The mass of the raven is 
The initial speed of the raven is 
The final speed of the raven is 
From the law of conservation of angular momentum we express this question mathematically as
Total initial angular momentum of both the Raven and the Gate = The Final angular momentum of both the Raven and the Gate
The initial angular momentum of the Raven is 
Note: the length is half because the Raven hit the gate at the mid point
The initial angular momentum of the Gate is zero
Note: This above is the generally formula for angular momentum of square objects
The final angular velocity of the Raven is 
The final angular velocity of the Gate is 
Substituting this formula


![\frac{1}{3} m_g L^2 w = m_r * \frac{L}{2} * [u_r - v_r]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20m_g%20L%5E2%20w%20%20%20%3D%20%20%20%20m_r%20%2A%20%20%5Cfrac%7BL%7D%7B2%7D%20%2A%20%5Bu_r%20-%20v_r%5D)
Where
is the angular velocity
Substituting value
![\frac{1}{3} (4.5)(2)^2 w = 1.2 * \frac{2}{2} * [5 - 1.5]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%284.5%29%282%29%5E2%20%20w%20%20%20%3D%20%20%20%201.2%20%2A%20%20%5Cfrac%7B2%7D%7B2%7D%20%2A%20%5B5%20-%201.5%5D)


