TOPIC OVERVIEW
Momentum
Momentum & Impulse
Momentum is mass in motion (p = mv). Impulse is how a force changes it over time, which is why airbags and crumple zones save lives.
Collisions & Conservation
In any closed system, total momentum stays the same. Use it to predict what happens when carts collide, balls bounce, or rockets launch.
STEP OVERVIEW
Solving Momentum Problems
Almost every momentum problem follows the same five moves. Master them and collisions become bookkeeping.
- Define your system and pick a positive direction.
- Write the total momentum before the event.
- Write the total momentum after the event.
- Set before = after (or use impulse J = FΔt = Δp if an outside force acts).
- Solve, then sanity-check signs, units, and whether kinetic energy should be conserved.
Practice Problems
Basic Difficulty
One-object momentum and impulse: find p, Δp, or the average force from a graph.
Intermediate Difficulty
Two-body collisions in one dimension, elastic vs. inelastic, plus explosions and recoil.
Challenge Difficulty
2D collisions, center-of-mass motion, and variable-mass systems like rockets.
COMPETITION CORNER
Momentum for F=ma and beyond
Competition problems love momentum because it turns messy forces into clean algebra. Expect center-of-mass tricks, ballistic pendulums, and collisions where you have to decide whether energy is conserved.
Center of Mass
If no outside force acts, the center of mass keeps cruising. Use it first.
Ballistic Pendulum
Momentum for the collision, energy for the swing. Never mix the two steps.
Explosions & Recoil
Start at rest, end at rest: total momentum is zero the whole time.