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:
Fnet,external = M d2R / dt2 = MA
where Fnet,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 miri / M (center of mass)
where mi and ri 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.