In many cases the net force acting on a system of particles is zero, or at least very close to it. For example, if you are on a nearly frictionless surface such as ice, the net force in the horizontal direction is zero and you will quickly slip and fall down. If you're wearing skates or rollerblades you might notice that there is little friction in the direction of motion so the net force acting in that direction can be quite close to zero. Since you are a system of particles, and are actually quite a sizeable number (if you don't mind me getting a bit personal here), then this is an example of a system (namely yourself on skates) that has zero net force acting on you in the horizontal direction. Other systems of particles, such as isolated atoms and molecules, provide another example of cases where often zero net force acts on the system. We'll talk a little bit more later about why even with friction, conservation of momentum can often still apply!
So let's derive conservation of momentum when 
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Eqn. 1.12 becomes
Now if the derivative of something is always zero, that something is a constant. This means that
That is the total momentum of a system is conserved, if the net force acting on the system is zero.
Let's talk about how poweful this conservation law is. It's kind of like energy conservation, inside the system, momentum can be transfered from one particle to another. But when this happens, the total momentum must stay unchanged.
Let's see how this works through an example.