A girl of mass M stands on the rim of a frictionless merry go-round of radius R and rotational inertia I that is not moving. She throws a rock of mass m horizontally in a direction that is tangent to the outer edge of the merry go-round. The speed of the rock, relative to the ground, is v. Afterward, the linear speed of the girl is

The initial angular momentum of the system is zero. The final angular momentum of the girl-plus-merry-go-round is I+MR2ω,which we will take to be positive. The final angular momentum we associate with the thrown rock is negative: -mRv, where v is the speed (positive, by definition) of the rock relative to the ground.Angular momentum conservation leads to0=I+MR2ω−mRv⇒ω=mRvI+MR2The girl's linear speed is Rω=mvR2I+MR2