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 perpendicular to the center of the line joining the atoms. Suppose that such a molecule in a gas has a speed of 5.96×102 m/s and that its rotational kinetic energy is two-thirds (2/3) of its translational kinetic energy. What then is the molecule's angular speed aboutthe center of mass?

Answer 1

`w= 8.0433*10^(12)rad/s`

Step-by-step explanation:

We need to define the variables.

`m= 5.30*10^(-26)Kg`

`I= 1.94*10^(-46)Kgm^2`

`v= 596m/s`

To use the energy conservative equation we need define
`K_r`, that is,

`k_r=(2)/(3) k_r`

So,

`(1)/(2)Iw^2 = (2)/(3) (1)/(2) mv^2`

`w^2 = (2mv^2)/(3*I)`

`w= \sqrt{(2(5.30*10^(-26))(596)^2)/((3(1.94*10^(-46))))}`

`w= 8.0433*10^(12)rad/s`