Past exam of the physics 1 paper of the University of Oxford / 2019 / 3 / a / Solution

Measure position $x$ along the ideal thin rod from its centre of mass. Its perpendicular distance from the inclined axis is $|x|\sin \alpha$, and its linear mass density is $M/L$. The moment of inertia is thereforeThis tends to zero for an axis along an infinitely thin rod and to $M{L}^2/12$ for a perpendicular central axis. A finite rod thickness would add a contribution absent from the stated thin-rod model.