Rotating molecules of a gas

Consider a thermally insulated cylinder containing ideal gas having triatomic rigid molecules having moment of inertia about center of mass $I = 3 \times 10^{-46} \text{ Kg} m^2$ each. The initial temperature is $T_{0} = 400K$ . Now , the gas is compressed by a factor of $n=4$ , such that in the time of compression, volume $V$ decreases linearly with time $t$ . Clearly, over this time the root mean square angular velocity, $\Omega = \sqrt{<\omega^2>}$ of particles would change . Find the value of $\sqrt{<\Omega^2>}$ (in m/s) over the course of the time of compression .

Details and assumptions

Boltzmann constant $k = 1.38 \times 10^{-23} J/K$