Tangent-axis inertia of a spherical shell
= Tangent-axis inertia of a spherical shell
{title2=$I=\frac{8\pi\rho}{15}(R_2^5-R_1^5)+MR_2^2$}
For uniform <density> between concentric radii $R_1,R_2$, subtract the missing solid core's central <moment of inertia> and then shift the axis by $R_2$. Here $M=4\pi\rho(R_2^3-R_1^3)/3$. The thin-shell limit gives $I=5MR_2^2/3$, while a full solid sphere gives $7MR_2^2/5$.