Similarly, B will exert a force on A, which will change A's momentum. These forces, by Newton's 3rd law, are equal and opposite, and therefore the changes in A's and B's momentum are equal and opposite:
In other words,
We now define the total momentum of the system as the sum of the momentum of A and B. We then have
This says that the total momentum of a system is conserved. This principle,
together with energy conservation, has many far-reaching consequences
in many areas of science.