Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 14A / a / Solution

Let $r$ be the cylindrical radius of the point of contact and $\varphi$ its azimuth. Rolling without slip or twist gives $|\omega |=v/a$ and thereforeup to an irrelevant additive constant. The factor $7/5$ combines translational and rotational inertia.