We study the response of a rotating monopole detector that is coupled to a massless scalar field which is described by a nonlinear dispersion relation in flat spacetime. Since it does not seem to be possible to evaluate the response of the rotating detector analytically, we resort to numerical computations. Interestingly, unlike the case of the uniformly accelerated detector that has been considered recently, we find that defining the transition probability rate of the rotating detector poses no difficulties. Further, we show that the response of the rotating detector can be computed exactly (albeit, numerically) even when it is coupled to a field that is governed by a nonlinear dispersion relation. We also discuss the response of the rotating detector in the presence of a cylindrical boundary on which the scalar field is constrained to vanish. While superluminal dispersion relations hardly affect the standard results, we find that subluminal dispersion relations can lead to relatively large modifications. © 2011 American Physical Society.