(II) A nonrotating cylindrical disk of moment of inertia I is dropped onto an identical disk rotating at angular speed co. Assuming no external torques, what is the final common angular speed of the two disks?

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The cylindrical disk of the moment of inertia I is rotating with an angular speed

Then a non-rotating cylindrical disk of the same moment of inertia I is dropped on the rotating cylinder.

As the net torque = 0, hence the angular momentum is conserved.

The coupled system now has rotational inertia

And let the final angular speed of this coupled system be