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.

Options

A. `(I _(1) omega _(1))/(I _(2))`
B. `(I _(2) omega _(1))/(I _(2) + I _(2))`
C. `(I _(1) omega _(2))/(I _(1) + I _(2))`
D. `((I _(1) + I _(2)))/( I _(2) omega _(1)`

Explanation

According toe the consevation of angular momentum `I _(omega) =` constant
When second disc is dropped on it and forms a unit.
`I_(1) omega _(1) = ( I_(1) + I _(2)) omega _(2)`
(angular momentum always constant )
`(I _(1) omega _(1))/( I _(1) + I _(2)) = omega _(2)`