Description of the paradox: We have a charged ring, which rotates at high speed. Since rotating charges produce cyclotron radiation, it emits photons. There is a toroidal mirror around the ring, spinning together with it. The mirror reflects the photons back inside, preventing them from escaping. The paradox lies in the question, where does the energy of the photons come from. There are two possible answers: 1. The energy comes from the rotational energy of the system. This way, the energy is conserved, but then, the system has to slow down its rotation, which contradicts the law of conservation of angular momentum. 2. The system does not reduce it's rotation. Angular momentum is conserved, but then, the energy of the photons comes from nothing, which contradicts thermodynamics.