An adaptive control scheme is proposed for stabilizing a planar rotor mounted on a magnetic bearing. The control strategy involves the concept of virtual autobalancing, where the control algorithm emulates the dynamics of a mechanical autobalancer by applying forces that are equivalent to the action of the autobalancer on the rotor. Equations of motion for a planar, torque-free, elastically suspended rotor equipped with an autobalancer are derived. Based on these equations, an adaptive controller for the magnetic rotor is formulated. The results are demonstrated in simulation.