The effect of uniform rotation on the equation of state of gluodynamics has been studied in lattice simulation. To this end, the system has been considered in the corotating reference frame, where the rotation can be modeled as an external gravitational field. The free energy of the studied system in the case of sufficiently slow rotation can be expanded in a power series in the angular velocity. The moment of inertia given by the second-order coefficient of this expansion has been calculated and its dependence on the temperature and the dimensions of the rotating system has been determined. Our results indicate that the moment of inertia of gluodynamics is negative up to the temperature T * ~ 1.5T$_{c}$, where T$_{c}$ is the critical temperature of the confinement/deconfinement phase transition, and becomes positive at temperatures T > T *. The negative moment of inertia has been attributed to the thermodynamic instability of the gluon plasma with respect to uniform rotation.