A disc of moment of inertia `I_(1)` is rotating freely with angular speed `omega_(1)` when another non-rotating disc of moment of inertia `I_(2)` is dropped on it. The two discs then rotate as one unit. Find the final angular speed.

Explanation

Here, initial angular momentum
`L_(1) = I_(1) omega_(1)`
Let `omega` be the final angular velocity of the combination. Therefore, final angular momentum.
`L_(2) = (I_(1) + I_(2)) omega`.
As `L_(2) = L_(1)`
`:. (I_(1) + I_(2)) omega = I_(1) omega_(1)`
`omega= (I_(1) omega_(1))/(I_(1) + I_(2))`