Angular Speed?

Question

The oxygen molecule, O2, has a total mass of 5.30 10-26 kg and a rotational inertia of 1.94 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 an O2 molecule in a gas has a translational speed of 580 m/s and the molecule has a rotational kinetic energy that is 2/3 of the translational kinetic energy of its center of mass. What then is the molecule's angular speed in rad/s about the center of mass. Thanks a lot for your help!

Answer 1

The translational kinetic energy is

1/2 m v^2

The rotational kinetic energy is

1/2 I w^2

where I is the moment of inertia and w the angular velocity.

"The rotational kinetic energy is 2/3 that of the translational kinetic energy"

1/2 I w^2 = ( 2 / 3 ) 1/2 m v^2

Plug in the values and solve for the angular velocity w.