The momemtum of a point particle of mass m going at velocity 
is
As a simple example, consider a ball with mass of 0.5 kg and with a velocity
in the positive x direction of 2 m/s, the magnitude of the ball's
momemtum is then 
.
Now if you have two particles, with masses 
and 
and velocities
and 
, the total momentum of these particles , 
is
That is, the momenta add normally as vectors are supposed to. As an example, consider the ball we just considered, and another ball, with mass 1 kg, travelling in the negative x direction with a speed of -1 m/s. One ball is going to the right, the other to the left. If you sum the two momenta together, you get a total momentum of zero.
Now how about for three particles? How about four particles? How about
45820349 particles? Hmmm, looks like a lot work. We can get around this
by
getting a little more sophisticated and write the definition
of the total momentum of N particles, of masses 
and
velocities 
as
