Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 585

our treatment of connected objects as a single object, provided that they
remain rigidly connected.) To stop the box, the Earth must push against
it with a force that is in the opposite direction that Moe pushed to start
it moving. However, we know that the “total amount” of pushing must be
the same, meaning the Earth must push back with a strong enough force,
or for a long enough duration (perhaps Moe's box rolls into a patch of tall
grass) to bring the momentum of the box down to zero. So you see that
whatever acceleration the Earth received as a result of getting Moe's box
in motion must always be exactly canceled by the force required to bring
the box to a stop.
But perhaps Moe's box does not come to a stop by pushing directly
against the Earth. Let's say it bumps up against Joe's box. Voila! We
have stopped Moe's box, and no force has been applied to the Earth. But
now, by Newton's third law, Joe's box must begin accelerating, and we are
back to where we started with a moving box that will continue moving
unless it receives a force to bring it to a stop. Eventually, the only way we
can stop this chain reaction started by Moe's push against his box is for
something, eventually, to push against the Earth.
We can generalize this idea even further. We are justified in treating
the entire Earth, and all of its moving parts, as a single particle with all
of its mass centered at some location known as the center of mass. (We
talk more about this special point in Section 12.3.2.) The pushing against
the Earth of people like Moe results in transfers of momentum between
the objects in the system. Each part will move around within this very
complicated system relative to the other parts and relative to the center of
mass of the system. However, the total amount of momentum of the entire
system is always a constant, unless there are external forces acting on the
system. This is known as the law of conservation of momentum.
The Law of Conservation of Momentum
The momentum of a system is constant unless external forces act on that
system.
The conservation of momentum is precisely what Equation (12.21)
is saying. It's certainly an experimentally verified fact, but it also fol-
lows naturally as a result of Newton's laws. Section 12.4 discusses how
to use this important law to simulate the collision of objects. However,
before we get to that, we need to take a closer look at the center of
mass.