Multi-User Multiple-Input Multiple-Output (MU-MIMO) is a pivotal technology in present-day wireless communication systems. In such systems, a base station or Access Point (AP) is equipped with multiple antenna elements and serves multiple active devices simultaneously. Nevertheless, most of the works evaluating the performance of MU-MIMO systems consider APs with static antenna arrays, that is, without any movement capability. Recently, the idea of APs and antenna arrays that are able to move have gained traction among the research community. Many works evaluate the communications performance of antenna systems able to move on the horizontal plane. However, such APs require a very bulky, complex and expensive movement system. In this work, we propose a simpler and cheaper alternative: the utilization of rotary APs, i.e. APs that can rotate. We also analyze the performance of a system in which the AP is able to both move and rotate. The movements and/or rotations of the APs are computed in order to maximize the mean per-user achievable spectral efficiency, based on estimates of the locations of the active devices and using particle swarm optimization. We adopt a spatially correlated Rician fading channel model, and evaluate the resulting optimized performance of the different setups in terms of mean per-user achievable spectral efficiencies. Our numerical results show that both the optimal rotations and movements of the APs can provide substantial performance gains when the line-of-sight components of the channel vectors are strong. Moreover, the simpler rotary APs can outperform the movable APs when their movement area is constrained.