= Polar second moment of area
{title2=$J_p=\int_A r^2\,dA$}
The polar second moment of a planar area about a perpendicular axis is the integral of squared distance from that axis over area. It has units $\mathrm{m^4}$ and equals the sum of second moments about two perpendicular in-plane axes through the same origin. For a disk of radius $a$, $J_p=\int_0^a2\pi r^3\,dr=\pi a^4/2$. It is geometric, not a mass <moment of inertia>; a uniform cylinder has axial mass moment $\rho LJ_p$.
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