Conservation of momentum

As a final point, we mention another fundamental conservation law, which is that of momentum (mass x velocity). Suppose that two objects, A and B, collide. A will exert a force on B, which will change B's momentum according to Newton's 2nd law

$\parbox{4.5in}{\vspace*{5pt} Force = change in momentum over time \vspace*{5pt}}$

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:

$\parbox{4.5in}{\vspace*{5pt} change in momentum of {\bf A} = - change in momentum of {\bf B}, \vspace*{5pt}}$

In other words,

$\parbox{4.5in}{\vspace*{5pt} change in momentum of {\bf A} + change in momentum of {\bf B} = 0, \vspace*{5pt}}$

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.