Using lattice simulations, we analyze the influence of uniform rotation on the equation of state of gluodynamics. For a sufficiently slow rotation, the free energy of the system can be expanded into a series of powers of angular velocity. We calculate the moment of inertia given by the quadratic coefficient of this expansion using both analytic continuation and derivative methods, which demonstrate a good agreement between the results. We find that the moment of inertia unexpectedly takes a negative value below the ``supervortical temperature''$T_s = 1.50(10) T_c$, vanishes at $T = T_s$, and becomes a positive quantity at higher temperatures. We discuss how our results are related to the scale anomaly and the magnetic gluon condensate. We point out that the negativity of the moment of inertia is in qualitative agreement with our previous lattice calculations, indicating that the rigid rotation increases the critical temperatures in gluodynamics and QCD.