What will be the direction and the rate of rotation of the single disk?

Question

Three disks are spinning independently on the same axle without friction. Their respective rotational inertias and angular speeds are I, omega (clockwise); 2I, 3*omega (counterclockwise); and 4I, omega/2 (clockwise). The disks then slide together and stick together, forming one piece with a single angular velocity. What will be the direction and the rate of rotation omega_net of the single piece?

Express your answer in terms of one or both of the variables I and omega and appropriate constants. Use a minus sign for clockwise rotation.

Answer 1

Conservation of angular momentum 'L'

L = I * (-omega) + 2I * (3 omega) + 4I * (-omega/2)

L = 3 I omega

Rotational inertia = I + 2I + 4I = 7I

omega_net = 3/7 omega (counterclockwise)