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 1.2 kg raven flying horizontally at 5.0 m/s flies into this door at its center and bounces back at 2.5 m/s in the opposite direction..What is the angular speed of the gate just after it is struck by the unfortunate raven?

ω = 1.82 rad/sec

Explanation:

Given

mass of the gate = 4.5 kg

distance between the hinge 1.5 m

mass of the bird = 1.2kg

velocity of the bird = 5 m/s  

The gate is rotates in circular motion

Inertia ot the gate = ×m×r²

                            =  ×4.5×1.5²

                               = 3.3 kg/m²---------(1)

momentum of the the rave = mv

                                       = 1.2×5

                                       = 6.0 kg

angular momentum of the gate = Iω

By conservation of energy

6. 0= 3.3×ω

ω= 6.0/3.3

= 1.82 rad/sec

from equation 1

I = 3.3 kg/m^2

ω = 1.82 rad/sec

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