Linear momentum is the quantity of motion an object has. It captures both how massive an object is and how fast it's moving — and crucially, which direction. A slow-moving freight train and a fast-moving baseball can have the same momentum. Both are equally difficult to stop.
Momentum is measured in kg·m/s, which is equivalent to N·s (Newton-seconds). You'll see both unit forms on the AP exam — they mean the same thing.
The formula for linear momentum is:
Mass m in kg, velocity v in m/s, momentum p in kg·m/s. Both mass and velocity enter linearly — double either one and you double the momentum. This is different from kinetic energy (K = ½mv²), where velocity is squared and therefore dominates.
A 0.145 kg baseball is thrown at 40 m/s to the right. A 2,000 kg car moves at 15 m/s to the right. Compare their momenta. Which is harder to stop?
Momentum inherits its direction from velocity. In one dimension, direction is handled entirely by sign. The most important habit in all of Unit 4: set your positive direction first, then apply it consistently to every object in the problem.
For a system of multiple objects, the total momentum is the vector sum of all individual momenta:
Signs determine whether momenta reinforce or partially cancel. A system where two equal-mass objects move toward each other at the same speed has exactly zero total momentum — even though both objects are moving.
Set mass and velocity for two objects. Watch how individual momenta combine as vectors — direction (sign) matters as much as magnitude.
Set both velocities in the same direction — Σp is large. Set them opposite — Σp can be small or even zero. A system can have zero total momentum even when both objects are moving.
Object A (3 kg) moves right at 6 m/s. Object B (5 kg) moves left at 2 m/s. Taking right as positive, find the total momentum of the system.
Two types of interactions define Unit 4. Both are analyzed using the same tool — momentum — and both conserve total momentum in isolated systems. The difference is what's happening physically.
Objects approach and interact. Internal forces between them during the brief interaction are far larger than any external force.
A single system breaks apart due to internal forces. Objects that were together (or at rest) fly apart.
A 4 kg object at rest explodes into two pieces. Piece A (1 kg) flies left at 12 m/s. What is the velocity of Piece B (3 kg)?