A clutch assembly consists of two cylindrical plates, Mass of A= 6.0 kg and Mass

Question

A clutch assembly consists of two cylindrical plates, Mass of A= 6.0 kg and Mass of B with an unknown mass. Both plates have the same radii R = 0.5 m. They are initially separated. Plate Mass of A is accelerated from rest to an angular velocity ?1 = 6.2 rad/s in time dt by a torque of 8.2 N·m.
Plate Mass of B, initially at rest and free to rotate without friction, is allowed to fall vertically so it is in firm contact with plate Mass of A. Before contact, Mass of A was rotating at constant ?1. After contact, the two plates rotate at a constant angular velocity ?2 = 3.8 rad/s. What is the mass of Mass of B? (answer in kg)

Explanation / Answer

using angulr momentum (I) conservation ,

6 x 0.52 /2   x 6.2  + m x 0.52 /2 x 0  = (6 x 0.52 /2 + m x 0.52 /2) X 3.8

0.75  x (6.2 - 3.8 )  = (0.125 x 3.8 )m

m = 3.78kg

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