The product of velocity and the mass of a particle is called as its linear momentum  .

The magnitude of linear momentum can be written as

                        P = mv

Or                    

Thus,               

Here, K is the kinetic energy of the particle. In according to the Newton's second law,

Thus,               

In case the external force applied to a body be zero, we have

Showing that in the absence of an external force, the linear momentum of a particle keeps constant. This is known as the law of conservation of linear momentum. The law may be extended to an object of particles or to the centre of mass of a system of particles. For example, for an object of particles it takes the form.

If net force on a system of bodies is zero, the vector addition of linear momentum of all the bodies keep conserved, or

If                     

Then,       

The same is the case for the centre of mass of a system of particles i.e., if

Thus, the law of conservation of linear momentum can be given to a single body, to a system of bodies or even to the centre of mass of the particles.  

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