Question #157541

What is virial theorem


1
Expert's answer
2021-01-25T14:03:37-0500

The virial theorem is a relation that connects the average kinetic energy of a system of particles with the forces acting in it. The virial G for the set of N point particles in mechanics is defined as:


G=pkrkG=\sum{\overrightarrow{p}_k\cdot\overrightarrow{r}_k} ,


where pk\overrightarrow{p}_k and r\overrightarrow{r} are the spatial vectors of momentum coordinates and coordinates for the k-th particle. For a stable system bound by potential forces, the virial theorem is


<T>=12Fkrk<T>=-\frac{1}{2}\sum{\overrightarrow{F}_k\cdot\overrightarrow{r}_k}


where <T><T> is the average total kinetic energy; Fk\overrightarrow{F}_k is the force acting on the k-th particle.








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