Virial Theorem

#Physics

$\displaystyle {\left\langle{K}\right\rangle}=-\frac{1}{2}{\left\langle{\sum_{\alpha}\vec{F}{\alpha}\cdot \vec{r}{\alpha}}\right\rangle}$

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

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

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