3.3.1—The principle of conservation of momentum

For a closed system with negligible external impulse, total momentum before an interaction equals total momentum after it: Σp_before=Σp_after.

Define the system and a positive direction first. Momentum is a vector, so opposite directions must carry opposite signs.

Two carts initially at rest apart can exchange equal and opposite momentum; for a collision, the signed total before and after must match.

Momentum is not automatically conserved for every chosen object: an external force can change that object’s momentum.