Compared to nanoscale friction of translational motion, the mechanisms of rotational friction have received less attention. Such motion becomes an important issue for the miniaturization of mechanical machinery that often involves rotating gears. In this study, molecular-dynamics simulations are performed to explore rotational friction for solid-state gears rotating on top of different substrates. In each case, viscous damping of the rotational motion is observed and found to be induced by the pure van der Waals interaction between the gear and the substrate. The influence of different gear sizes and various substrate materials is investigated. Furthermore, the rigidities of the gear and the substrate are found to give rise to different dissipation channels. Finally, it is shown that the dominant contribution to the dissipation is related to the excitation of low-frequency surface phonons in the substrate.