A thin massless horizontal pipe rotates about a vertical axis with angular speed ω as shown in the figure. A small bug, located at a distance r from the axis, starts crawling inside the pipe at constant speed v (relative to the pipe). Because of the bug, the motor must develop the power

Question

A thin massless horizontal pipe rotates about a vertical axis with angular speed ω as shown in the figure. A small bug, located at a distance r from the axis, starts crawling inside the pipe at constant speed v (relative to the pipe). Because of the bug, the motor must develop the power
Pm=Cmω2vr
in order to keep the system rotating at constant angular speed ω. Determine the numerical coefficient C. m is the mass of the bug.