Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 11C / a / i / Solution

The moment of inertia about an axis iswhere $r_{\perp }$ is the perpendicular distance to the axis. The disc mass isTo leading order in $\delta /r$, the distance from the $x$-axis is $|y|$. Using polar coordinates in the disc,