A magnetic torque is induced by motions of a cylindrical metal shell that is being levitated around an alternating‐current filament—a suspension device analyzed previously for the motionless case. This kinetic magnetic torque is calculated for shell‐filament configurations in which the shell rotates on its own axis while revolving in circular orbits about the parallel current axis. The calculated torque is given numerically over a wide range of device parameters via a set of universal curves, with analytic formulae for limiting cases. The torque results are used to assess the dynamics of the suspension under various conditions, including external magnetic spin damping and extraneous orbital momentum generation.