Moment of inertia of a uniform annulus ($I=\frac{M}{2}(a^2+b^2)$)

A uniform planar annulus of outer radius $a$, inner radius $b<a$ and mass $M$ has surface density $M/[\pi (a^2-b^2)]$. Integrating $r^2$ over its mass gives the axial moment of inertia $I=M(a^2+b^2)/2$. Subtracting the inner disc from a complete disc gives the same result, provided their surface densities match.

// Target: electromagnetism.bigb