We will begin with the statement of the principle of conservation of momentum.

When we talk about the total momentum of a system, we are talking about the sum of all of the momentum vectors of all the particles in the system. Since this is a vector calculation, it’s possible that the total momentum of the system is zero even though there are particles moving around in it. We also need to make sure that we are using the same frame of reference for both the before and after calculations.

An isolated system is a system that has no external forces acting on it. You want to imagine that you’ve isolated all of the components of the interaction to some far-off corner of space, far from everything. When working on problems, this is simple enough to do because we tend to only include the objects that are interacting in our calculations. In practice, this mostly means keeping people away from the experiment and making sure that the interaction happens horizontally to avoid the influence of gravity.

It is important to remember that this is talking about the influence of external forces. Objects within the system can have all sorts of complicated interactions with each other without violating the conservation of momentum.