As we know, the linear momentum of a particle is defined as , where m is the mass and is the velocity, the momentum of an N particle system is the vector sum of the momenta of the N particles.
If the external forces acting on the system add up to zero, the centre of mass moves with constant velocity.
Hence, the principle of conservation of linear momentum states that the linear momentum of a system remains constant if the external forces acting on the system add up to zero.
