Frequency domain analysis of moving imagery is quite informative with respect to spectral estimation and coding techniques based on short-time Fourier transform and wavelet transform. The frequency domain analysis for translations [see the first and the third author, IEE Trans. Pattern Anal. Machine Intell. 15 (1993) and the first author and \textit{G. Nalesso}, Report DEI 90/16, Dipartimento di Elettronica e Informatica, Universita' di Padova, Padova (1993)] is extended to the case of rotations. The relationship between the Fourier transform of a planar object and the Fourier transform of the same object rotating with polynomial time-dependence is studied. The specific spectral features of the rotating objects depend on the angular periodicity of the planar objects. Angular velocity and angular acceleration affect the Fourier transform of the rotating object with quite distinctive effects. Using the ideas in the above cited paper of the first and the third author objects rotating with piecewise polynomial (instead of polynomial) time-dependence could also be studied. As a next step the authors intend to study the frequency domain analysis of simultaneous rotation and translation.