Physics · Rotational Mechanics

A thin rod of mass M and length a is free to rotate in a horizontal plane about a fixed vertical axis passing through point O. A thin circular disc of mass M and of radius a/4 is pivoted on this rod with its center at a distance a/4 from the free end so that it can rotate freely about its vertical axis. Assume that both the rod and the disc have uniform density and remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity Ω and the disc rotating about its vertical axis with angular velocity 4Ω. If the total angular momentum of the system about the point O is M a2 Ω48 n, the value of n is: