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

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Angular momentum is conserved here because there's no external net forces acting so the initial angular momentum of the system is the moment of inertia of one disk times its angular velocity and then after the disk is dropped on the identical disk below the moment of inertia of the system is gonna be 2 times the moment of inertia of one disk because since they are identical when you combine them together— well each disk has the same moment of inertia and so— the moment of inertia of the system of the two combined will be 2 times the moment of inertia of one of them. And there will be some different angular velocity when the two are combined but the angular momenta will be the same so L f equals L i. And so we have 2Iω f equals Iω and divide both sides by I and divide both sides by 2 as well and we see that the final angular velocity will be half of the initial angular velocity of the disk before it was dropped.