Aboy of mass m is standing on the edge of a merry-go-round platform, which is initially rotating with a constant rotational velocity ωi (initial state). the rotational inertia of the merry-go-round is i, and the radius of the platform is r. after the boy steps down from the platform, tangentially to its edge, the merry-go-round continues rotating with a smaller rotational velocity ωf, and the boy continues moving away from the platform with constant speed v (final state).

question: derive the expression for ωf in terms of the relevant quantities. express your answer in terms of i, m, r, v, and ωi.