Rotational energy of diatomic molecule

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The discussion focuses on the rotational energy of a diatomic molecule modeled as two atoms connected by a massless rod. The equation for rotational energy is derived from the moment of inertia, which is defined as m*L^2, where m is the reduced mass and L is the length of the rod. The rotational energy is calculated assuming rotation about an axis through the center of mass, perpendicular to the line connecting the atoms. Additionally, the conversation touches on calculating the kinetic energy associated with the vibrational motion of the atoms when the molecule is not rotating. Understanding these concepts is essential for analyzing the dynamics of diatomic molecules.
nikolafmf
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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 appreciate any help.


Nikola
 
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What is the moment of inertia of a diatomic molecule about an axis passing through the center of mass?
 
Gokul43201 said:
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?
 

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