Relativistic energy shift of particles passing through a rotating track

The relativistic energy shift for particles with mass m passing through a carved path with arbitrary shape and reflecting walls inside a rotating disc is considered. The absorber of particles is either rotating with disc or is outside of disc and is stationary in the Lab frame. It is shown that, for the case of rotating absorber, the energy shift is independent of mass of particles and the shape of the track. In the case of the stationary absorber, the only relevant parameter of the shape of the track is the angle at which the track ends at the edge of the disc. For the rotating absorber, the leading order of the energy shift is (v/c)^2 , while for the stationary absorber and the non-radial ending tracks, the energy shift has a correction of the order ( v / c ) as well.