Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics IV / 6 / b / ii / Solution

The rod and disc contribute restoring torques $-mg(\ell /2)\sin \theta$ and $-Mgd\sin \theta$, respectively. Using i in the rotational equation of motion givesOnly the disc's center of mass enters its gravitational torque; its finite radius enters its moment of inertia. The formula is also regular at $M=m$, although the source happens to exclude that value.