 Rotational magnetic damping of a square wire loop

A thin square loop rotating about a central in-plane axis has $\mathcal{I}=m{a}^2/6$. With ohmic current and decay slow compared with a rotation, the averaged torque is $-B^2{a}^4\omega /(2R)$. Its angular-speed decay time is $mR/(3B^2{a}^2)$; its kinetic-energy decay time is half that value.