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Example: The Moment of Inertia of a Diatomic Molecule
What is the moment of inertia of a diatomic nitrogen molecule $N_{2}$ around its center of mass. The mass of a nitrogen atom is $2.3$ x $10^{-26}$ kg and the average distance between nuclei is $1.5$ x $10^{-10}$ m. Use the definition of moment of inertia carefully.
Facts
Assumptions and Approximations
Lacking
Representations
Solution
For two masses, $I = m_{1}r^{2}_{\perp1}$ + $m_{2}r^{2}_{\perp2}$. The distance between masses is d, so the distance of each object from the center of mass is $r_{\perp1} = r_{\perp2} = d/2$. Therefore:
$I = M(d/2)^{2} + M(d/2)^{2} = 2M(d/2)^{2}$
$I = 2 \cdot (2.3 x 10^{-26}kg)(0.75 x 10^{-10}m)^2$