We study the implications of quantum fluctuations of a dispersive medium,

under steady rotation, either in or out of thermal equilibrium with its

environment. A rotating object exhibits a quantum instability by dissipating

its mechanical motion via spontaneous emission of photons, as well as internal

heat generation. Universal relations are derived for the radiated energy and

angular momentum as trace formulas involving the object's scattering matrix. We

also compute the quantum noise by deriving the full statistics of the radiated

photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy

generation is quantified, and the total entropy is shown to be always

increasing. Furthermore, we derive a Fokker-Planck equation governing the

stochastic angular motion resulting from the fluctuating back-reaction

frictional torque. As a result, we find a quantum limit on the uncertainty of

the object's angular velocity in steady rotation. Finally, we show in some

detail that a rotating object drags nearby objects, making them spin parallel

to its axis of rotation. A scalar toy model is introduced in the first part to

simplify the technicalities and ease the conceptual complexities; a detailed

discussion of quantum electrodynamics is presented in the second part.