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.

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 $10^{-10}m)^2$

$I = 2.6$ x $10^{-46} kg \cdot m^2$