Past exam of the physics 1 paper of the University of Oxford / 2017 resit / 11 / b / Solution

For a uniform disk, the surface mass density is $\sigma =m/(\pi a^2)$. Integrate concentric annuli of mass $dm=2\pi \sigma rdr$ about the central perpendicular axis:The result is specific to a uniform thin disk and that axis; it is not the diameter-axis moment of inertia, which is $m{a}^2/4$ by planar symmetry and the perpendicular axis theorem.