Question

When we say that momentum is conserved for an isolated system, what specifically does that mean?

Answer 1

An isolated system means there will be no external force acting on the system.

The system can have many objects and they can apply force to eachother (by colliding with themselves). But net external force on the whole system is zero.

Now according to Newton's law, applied force = rate of change of momentum. This means, no force implies no momentum chenge

As there is no external force acting, so the net momentum of the system (i.e. the sum of individual momentums of the objects of the system) will be unchanged.

This is what we mean by momentum is conserved for an isolated system.

Note that, the momentums of the individual objects of the system are not conserved, as they can apply force on each other (internal collision).

This is the reason we can always apply momentum conservation in the collision (elastic or inelastic) problem, as there is no external force acting.