A diatomic gas molecule has a mass of 2.01 x 10-26 kg and a rotational inertia of 3.37 x 10-46 kgm2 about an axis through the center of the line...

A diatomic gas molecule has a mass of 2.01 x 10-26 kg and a rotational inertia of 3.37 x 10-46 kg·m2 about an axis through the center of the line joining the atoms and perpendicular to that line. Suppose the center of mass of the molecule has a translational speed of 677 m/s and the molecule has a rotational kinetic energy that is of the translational kinetic energy of its center of mass. What then is the molecule's angular speed about the center of mass?