Momentum has no memory

Why this rule exists

Momentum, p = mv, is conserved because the laws of physics do not care where you are: space is uniform, and that translational symmetry guarantees the total momentum of an isolated system is fixed regardless of how its parts interact. "No memory" means the conservation depends only on the present total, not on the history that produced it. Internal forces come in equal and opposite pairs by Newton's third law, so they cancel in the sum and cannot change the whole.

In practice

Draw a boundary, confirm no net external force acts, then write total momentum before equal to total momentum after — as vectors, component by component. Collisions are the classic case: you need not know the messy forces during contact, only the momenta entering and leaving. Momentum is conserved even when energy is not, as in inelastic collisions, which makes it the more robust tool when objects stick or deform.

Example

A stationary rifle (M) fires a bullet (m).
Total momentum before = 0.

After: bullet moves at v, rifle recoils at V.
Conservation: 0 = m·v + M·V

Solve for recoil velocity:
V = −(m/M)·v

Minus sign: rifle moves opposite the bullet.

When it doesn't apply

Conservation fails the moment an external force acts on the system: gravity, a wall, friction from outside all inject momentum, so enlarge the boundary to include whatever supplies the force. Momentum is a vector, so it can be conserved in one direction while an external force changes another.