The recent availability of accurate observations of rotational ground motions has reopened interest in understanding near-fault characteristics of such motions in the context of strong ground motion and earthquake engineering. In order to investigate source and structure-dependent variations of rotational motions, we simulate several M 7 earthquakes with varying source scenarios on the Newport–Inglewood (NI) fault embedded in the 3D Los Angeles basin using a finite-difference method in the frequency range up to 0.5 Hz. We use a precalculated database with several hundred numerical Green’s functions for a discretized model of the NI fault that allows arbitrary finite-fault scenarios to be synthesized by superposition. We investigate source and basin effects on the rotational part of ground motion (namely maximum peak ground rotation rates and their variations) and compare them with the corresponding values of translational motion. Our main conclusions are: (1) the pure strike-slip source mechanism leads to larger rotation rates around the vertical axis than around the horizontal ones; (2) variation of hypocenter introduces more scatter on ground rotation rate than variations of slip history; (3) the coprocessing of translation and rotation recordings might reveal information on local velocity structure as indicated by plane-wave theory; and (4) the attenuation of accelerations (horizontal components) and rotation rate (vertical component) with distance from the fault are very similar, suggesting that similar expressions (as a function of distance) as for the peak accelerations can be adopted for the peak rotation rates when determining their attenuation relations.