Virial Theorem

$⟨K⟩=-\frac{1}{2}⟨\sum _{\alpha }{\vec{F}}_{\alpha }\cdot {\vec{r}}_{\alpha }⟩$

• $⟨K⟩$ is the average kinetic energy of a system of particles in equilibrium
• $F_{\alpha }$ is the force on the $\alpha$th particle
• $r_{\alpha }$ is the position vector for the $\alpha$th particle
• RHS of equation is the Virial of the system
• Assumes a system that has come to equilibrium

$K=-\frac{U}{2}$

• The total kinetic energy of a bunch of particles is dependent on the total potential energy of the system