A runner of mass m runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude v. The turntable is rotating in the opposite direction with an angular velocity of magnitude omega relative to the earth. The radius of the turntable is r, and its moment of inertia about the axis of rotation is I.
Find the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can treat the runner as a particle.)