In this talk, I will present results obtained using the hyperboloidal approach to compute the quasinormal modes and pseudospectra of a rotating analog black hole described by the draining bathtub model. Within this framework, we investigate how rotation affects the spectral stability of the system. The analysis shows that, as rotation increases, prograde overtones migrate toward the same region of the pseudospectrum occupied by the fundamental mode, which is known to be more stable under certain perturbations of the gravitational potential. This correlation suggests that the prograde overtones might also acquire greater robustness. A direct perturbative analysis confirms this hypothesis, indicating that angular momentum may mitigate spectral instabilities in dissipative systems.