Question

A disk with moment of inertia I relative to a vertical axis through its center is dropped onto another disk with moment of inertia equal to 2I which is rotating with angular velocity . Find the final angular velocity in terms of .

Answer 1

0.66 times the original one

Step-by-step explanation:

A disc of moment of inertia 2I is rotating with angular speed ω. Now another disc of moment of inertia I dropped on it and the new angular velocity is ω'.

By use of conservation of angular momentum

2I x ω = (2I +I ) x ω'

ω' = 2ω/3

ω' = 0.66 ω

Thus, the new angular velocity becomes 0.66 times the original one.