Consider a system of N particles of masses m1, m2, m3,------------ mN.
Let a, b, c, ……………. represent the particle numbers ranging from 1 to 
.
Let the particle a be acted upon by some external force 
and by an internal force 
from every other particle in the system.
According to Newton's second law,
According to Newton's third law,
For any ath particle
Substituting a = 1, 2,……….. N. We have N equations. Adding them all,
The position vector of the centre of mass of the whole system is given by,
Where M = m1+m2+-------mN
is the weighted average of the position vectors of the particles of the system. It moves according to the equation of motion.
