Answer:
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 = [tex]\frac{1}{3}[/tex]×m×r²
= [tex]\frac{1}{3}[/tex]×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
