The oxygen molecule has a mass of `5.30 xx 10^(-26) kg` and a moment of inertia of `1.94 xx 10^(-46) kg m^(2)` about an axis through its centre perpendicular to the line joining the two atoms. Suppose the mean speed of such a molecule in a gas is `500 m//s` and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

Explanation

Rotational kinetic energy `=(2)/(3)xx` Translational kinetic energy
i.s, `(1)/(2) I omega^(2)=(2)/(3)xx(1)/(2) mv^(2)`
So `omega= v sqrt((2)/(3)(m)/(I))`
`=50xx sqrt((2)/(3)xx(5.30xx10^(26))/(1.97xx10^(-46)))`
`=6.75xx10^(12) "rad" s^(-1)`.