A disk with moment of inertia `I_1` rotates about frictionless, vertical axle with angular speed `omega_i` A second disk, this one having moment of inertia `I_2` and initial not rotating, drops onto the first disk (Fig.) Because of friction between the surfaces, the two eventually reach the same angular speed `omega_f`. The value of `omega_f` is.
.

Options

A. `(I_1 + I_2)/(I_1) omega_i`
B. `(I_1)/(I_1 + I_2) omega_i`
C. `(I_1 + I_2)/(I_2) omega_i`
D. `(I_1)/(I_2) omega_i`

Answer

B

Explanation

(b) From conservation of angular momentum for the isolated system of two disks :
`(I_1 + I_2) omega_f = I_i omega_i` or `omega_f = (I_1)/(I_1 + I_2) omega_i`.