Self-sustained vibrations which can appear in mechanical systems often limit the performance of such systems or can even cause failure or damage to them. Although a lot of theoretical research has been done on vibrations in flexible rotor systems, a limited number of papers are available including experimental results on the interaction between different types of vibrations. Here, we address friction-induced vibrations in flexible mechanical systems, lateral vibrations caused by mass-unbalance in rotor systems and the interaction between those two types of vibrations. Analysis of a set-up, when both torsional and lateral vibrations are present, leads to the conclusion that friction-induced torsional vibrations and torsional vibrations due to coupling between torsional and lateral dynamics may appear. Furthermore, if mass-unbalance is present in the system, the amplitude of friction-induced vibrations and the region in which these vibrations occur, both decrease compared to the situation without mass-unbalance. Moreover, it is shown that if the mass-unbalance is large enough then torsional vibrations can disappear entirely.