A ballerina with moment of inertia $I$ stands on frictionless ice, spinning at angular velocity $\omega_0$ about her vertical body axis. In her outstretched hand she holds a small ball of mass $m$ at horizontal distance $R$ from her axis, co-rotating with her. She opens her hand and lets the ball go — no push, no twist. The ball falls under gravity, lands on the ice, and slides freely. Long after the ball has landed, what is the ballerina's angular velocity about her body axis?