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3.13: The Virial Theorem
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/03%3A_Systems_of_Particles/3.13%3A_The_Virial_Theorem
The virial Equation tells us whether the cluster is going to disperse or collapse.
2.1: Definition of Moment of Inertia
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/02%3A_Moments_of_Inertia/2.01%3A_Definition_of_Moment_of_Inertia
The quantity $m_{i} r_{i}^{2}$ is the second moment of the $i$ th mass with respect to (or "about") the axis, and the sum $\sum m_{i} r_{i}^{2}$ is the second moment of mass of all the mas...The quantity $m_{i} r_{i}^{2}$ is the second moment of the $i$ th mass with respect to (or "about") the axis, and the sum $\sum m_{i} r_{i}^{2}$ is the second moment of mass of all the masses with respect to the axis. But the question should be asked: "What is the purpose of calculating the squares of the distances of lots of particles from an axis, multiplying these squares by the mass of each, and adding them all together?

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