Stability of a rotating disk under rotating positive-definite damping forces is investigated analytically. The stability boundary is located exactly in parameter space by the criterion that at least one non-trivial periodic solution is necessary at every boundary point. The stable region of parameter space is identified through perturbation of a Galerkin solution. A non-trivial periodic solution is shown to exist only when damping forces are not generated with respect to that solution. Instability in the disk-damping system occurs when the wave speed of any mode in the undamped disk, when observed on the disk, is less that the speed of the damping force relative the disk. The instability occurs independent of the magnitude of the force and the definition of the positive-definite damping operator.