Solution
= Solution
<Rolling without slipping> gives $\omega^2=g/[(L-r)(1+2R^2/(5r^2))]$. With the supplied dimensions, $T\simeq80.5\,\mathrm s$ and the maximum centre-of-mass speed for a $10\,\mathrm{mm}$ rise is $0.0349\,\mathrm{m\,s^{-1}}$.
Full derivation: <past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2010/paper-2a/section-c/c11/solution>.