Past exam of the mathematics course of the University of Oxford / 2021 / Prelims / Mathematics IV resit / 6 / a

The solid cylinder has constant mass density $\rho =m/(\pi a^{2}l)$. A thin cylindrical shell of radius $s$ and thickness $ds$ has mass $dm=2\pi \rho lsds$. Its contribution to the axial moment of inertia is $s^{2}dm$. ThereforeThe attached wheels are massless, so they add no moment of inertia. This is the moment of inertia of a uniform solid cylinder about its central longitudinal axis of rotation.