An oxygen molecule has a mass of `5.30xx10^(-26)` kg and a moment of inertia of `1.94xx10^(-46)kgm^2` about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is `500ms^(-1)` 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

Inertia of the system of atoms, `I=(m/2)r^2+(m/2)t^2`
`I=mr^2`
`:.r=sqrt(I/m)=sqrt(1.94xx10^(-46)/(5.30xx10^(-26))=0.60xx10^(-10)m`
given `1/2(mr^2)(omega^2)=1/3mv^2`
i.e `1/2(mr^2)(omega^2)=1/3mv^2" "omega^2=2/3(v^2)/(r^2)`
i.e `omega=v/rsqrt(2/3)` i.e. `omega=(0.8165xx500)/(0.6xx10^(-10))=680.4xx10^(10)`
i.e `omega=6.804xx10^(12)rads^(-1)`