Isolated and non-isolated systems: Momentum? I'm having a difficult time understanding why two billiard balls colliding is an isolated system, yet a car crashing into a wall is a non-isolated system. Does it really only have to deal with the fact that the car crash has friction as an "outside" force -- but doesn't the pool table have friction? I'm unsure if what I'm saying makes any sense, but any clarifications on this would help me understand how to differentiate between these two types of systems. Thanks!
 A: It all depends on what you want to study. The billiard balls are generally viewed as an isolated system for the purposes of explaining elastic collisions, but you could as well introduce friction with the pool table, and the consider the system balls+table as the isolated one. This just means you have to consider the friction.
In the case of the car hitting the wall, since the wall is grounded to Earth, as it is generally in this example, you cannot assume the system car+wall is isolated, however you could assume the system car+wall+Earth is. So when the car hits the wall, it is crashed as a result of the different deformation resistance it has w.r.t the wall. But if the wall were not grounded, and you consider the collision car-wall in say, space, the you could say car+wall is an isolated system.
A: The concept of an isolated system is an approximation. Like all approximations, it applies to some systems better than others.
A billiard ball feels only a weak frictional force in the form of rolling resistance, whereas a wall typically has foundations buried in the ground which can provide a strong resistive force. Thus, the former system is closer to the idealised isolated system, so conservation of momentum holds more faithfully.
The time of action of the frictional forces also matters. If the motion of a billiard ball is studied during a millisecond where the collision takes place, the friction will be negligible. If the motion is studied over several seconds, it will be significant.
In general, to estimate whether frictional forces are relevant, estimate the typical frictional force $F$, the timescale $t$ and the typical momentum changes of interest $\Delta p$. If $Ft \ll \Delta p $ then the system is well-described as "isolated".
A: In any of the isolated system, no outer force is acting. The sum of momentum, or we can say net force, remains unchanged, if any change in velocity occurs. If any outer force is acting on the system, it will be considered as non-isolated system.
