Rotating modes are instabilities which are commonly observed in swirling flows. This paper shows that in complex-geometry combustors, such modes can appear under both cold and reacting conditions but that they have different sources: while the cold flow rotating mode is essentially hydrodynamic and corresponds to the well-known PVC (precessing vortex core) observed in many swirled unconfined flows, the rotating structure observed for the reacting case inside the combustion chamber is not hydrodynamically but acoustically controlled. The two transverse acoustic modes of the combustion chamber couple and create a rotating motion of the flame which leads to a self-sustained turning mode which has the features of a classical PVC but a very different source (acoustics and not hydrodynamics). These results are obtained using two complementary tools: compressible LES (large-eddy simulation) which solve the turbulent flow and the acoustics simultaneously (but at a high cost) and the Helmholtz solver which extracts only the acoustic modes using the mean flow field and linear acoustics assumptions.