We have seen that we can write Newton’s 2^nd law in terms of linear momentum in the form

From this it follows that, if the net force acting on an object (or system of objects) is zero, then the change in momentum of that object (or system of  objects) must also be zero.

Thus, in this case, the initial and final momenta must be the same!  This also  holds true for a system of particles, in which case we must be careful to consider the total initial and final momenta of the system:

Since momentum is a vector quantity, we must be careful to add the momenta by components. The single equation above is therefore equivalent  to the two equations

The equation above is the important statement of the conservation of linear momentum .  It will be very important to keep in mind that the momentum of a system will be conserved (that is, its value won’t change) as long as the net external force acting on the system is zero (or, equivalently, as long as the  external forces such as gravity acting on the system are negligible).