The linear momentum of a particle is defined as
p = m v
Let us also recall that Newton’s second law written in symbolic form for a single particle is
For the system of n particles, the linear momentum of the system is defined to be the vector sum of all individual particles of the system,
P = p1 + p2 +…..+ pn
P = m1v1 + m2v2 +…..+ mnvn
Comparing this with eq(4)
P = M V
Thus, the total momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its centre of mass.
Differentiating this eq P = M V , with respect to time,
Comparing Eq.(7) and Eq.(6),
This is the statement of Newton’s second law extended to a system of particles.
Suppose now, that the sum of external forces acting on a system of particles is zero. Then from Eq.(8)