A

system of particles of total mass

**M** has associated with it a point called the

center of mass to

Newton's laws of motion apply as they do to a

point particle:

**F**_{net,external} = M d^{2}**R** / dt^{2} = M**A**

where **F**_{net,external} is the net external force (duh) on the system and **A** the acceleration of the center of mass. The position **R** of the center of mass is given by:

***R** = **Σ **m_{i}**r**_{i} / M (center of mass)
where *m*_{i} and **r**_{i} represent the masses and positions of the individual particles in the system. For continuously distributed matter, the center of mass position nis given by an integral:

**R** = 1/M ∫ **r** *dm*

where the integration is taken over the entire system. That the center of mass concept is useful is a consequence of Newton's third law, which requires that internal forces cancel in pairs, leaving the overall system motion detrmined only by external forces.

**This method is elaborated in center of mass.*