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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jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.