A child of mass m is standing at the edge of a carousel. Both the carousel and the child are initially stationary. The carousel is a large flat, uniform disc of mass M, and radius R, which turns on a frictionless pivot at its center. It has moment of inertia /= MR/2. The child is very small compared to the carousel. The child starts to run around the edge of he carousel at speed v. The direction of child is counter-clockwise when the carousel is viewed from above. Taking the -axis as upwards, what is the angular velocity of the carousel after the child has started running? Initial: Child and Carousel at rest R Final: Child running counterclockwise with speed v R