Rotational energy of diatomic molecule

[nikolafmf]

Hi,

I consider harmonic model of diatomic molecule: two atoms connected with a massless rod. Let one axis be along the rod, other two perpendicular to it. Let rotational velocity have components only trough perpendicular axes. In one book it is said that rotational energy of such diatomic molecule is 1/2*m*r^2*(omega(1)^2+omega(2)^2), where m is reduced mass, r is the length of the rod, omega(1) and omega(2) are the components of the rotational velocity.

Where this reduced mass come from? How can I derive this equation? I would appriciate any help.

Sincerely,
Nikola

[Gokul43201]

What is the moment of inertia of a diatomic molecule about an axis passing through the center of mass?

[nikolafmf]

What is the moment of inertia of a diatomic molecule about an axis passing through the center of mass?

First, thank you for your question which led me to the answer :).

The moment of inertia is m*L^2. So, when calculating rotational energy, author implicitely assumes that molecule rotates about an axis passing through its center of mass and is perpendicular to line conecting atoms. Why should be so? Why not another axis?

Conected with this problem is calculating kinetic energy of the molecule due its vibration. Let say that molecule doesn't rotate, its center of mass doesn't move, but only atoms move to and from each other (they vibrate). We know the mass of each atom and their relative velocity (but not their absolute velocity). How could I calculate kinetic energy due to this motion?