  The effect of angular momentum conservation in microcanonical thermodynamics
is considered. This is relevant in gravitating systems, where angular momentum
is conserved and the collapsing nature of the forces makes the microcanonical
ensemble the proper statistical description of the physical processes. The
microcanonical distribution function with non-vanishing angular momentum is
obtained as a function of the coordinates of the particles. As an example, a
simple model of gravitating particles, introduced by Thirring long ago, is
worked out. The phase diagram contains three phases: for low values of the
angular momentum $L$ the system behaves as the original model, showing a
complete collapse at low energies and an entropy with a convex intruder. For
intermediate values of $L$ the collapse at low energies is not complete and the
entropy still has a convex intruder. For large $L$ there is neither collapse
nor anomalies in the thermodynamical quantities. A short discussion of the
extension of these results to more realistic situations is exposed.
