Question

A square weightless frame ABCD with the side a is rotating around the side AB with the constant angular velocity ω1. A uniform disk of radius R and mass m is rotating around the frame’s diagonal AC with the constant angular velocity ω2. The center of the disk coincides with the center of the frame. Assuming ω1 = ω2 = ω find

a. The kinetic energy of the system.
b. The magnitude of the torque that needs to be applied to the axis AB to keep it (the axis AB) still.

Answer 1

Answer:

1) KE of the system = 1/2(Iw^2)

2) the torque T that must be applied to keep it still must be equal to the torque of rotation. This is equal to

T = (Iw^2)/2©

Where;

I = moment of inertia of the body

W = angular velocity of the body

© = angle of rotation in rad

Explanation:

Detailed explanation and calculation is shown in the image below