A brave child decides to grab onto an already spinning merry‑go‑round. The child is initially at rest and has a mass of 31.5 kg. The child grabs and clings to a bar that is 1.25 m from the center of the merry‑go‑round, causing the angular velocity of the merry‑go‑round to abruptly drop from 51.0 rpm to 17.0 rpm . What is the moment of inertia of the merry‑go‑round with respect to its central axis?