Everything you need to master Unit 4 — momentum (p = mv), impulse, the impulse-momentum theorem, conservation of momentum, and elastic vs. inelastic collisions. The exam loves these problems.
10–15% of the AP exam
7 study resources
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Seven free resources for Unit 4 — pick the one that fits how you learn.
Unit 4 introduces linear momentum — a vector quantity (p = mv) that turns out to be more fundamental than kinetic energy for analyzing collisions. While energy can change forms, momentum is conserved in EVERY interaction where no external force acts. This makes collision problems much easier than they look.
The College Board breaks Unit 4 into 4 topics: (4.1) Linear Momentum and the object/collision/explosion models, (4.2) Change in Momentum and Impulse (J = FΔt = Δp), (4.3) Conservation of Linear Momentum, and (4.4) Elastic and Inelastic Collisions. Topic 4.3 is the heart of the unit — momentum is conserved whenever no net external force acts on the system.
Unit 4 makes up about 10–15% of the AP Physics 1 exam. Even though it's not the heaviest unit, momentum concepts feed directly into Unit 5 (where angular momentum is the rotational analog) and Unit 6 (rotational systems).
Key terms preview
A taste of what you'll find in The Essentials and Flashcards.
Linear Momentum
p = mv. A vector quantity equal to mass times velocity. Same direction as velocity.
Impulse
J = F·Δt. The product of force and time. Equals the change in momentum (Δp).
Impulse-Momentum Theorem
J = Δp. The impulse on a system equals its change in momentum. Connects forces and motion through time.
Conservation of Momentum
When no net external force acts, total system momentum stays constant. p_i = p_f.
Elastic Collision
A collision in which the total kinetic energy of the system is conserved (KE_i = KE_f).
Inelastic Collision
A collision in which kinetic energy decreases (converted to heat, sound, deformation). Momentum is still conserved.
1. Momentum is conserved when no external force acts
For any closed system with no net external force, the total momentum stays constant. Two carts colliding, a rocket blasting off, ice skaters pushing apart — all are explained by "p_i = p_f." Internal forces (the ones between objects within the system) come in third-law pairs and cancel out, leaving momentum unchanged.
2. Impulse equals change in momentum
Impulse (J = F·Δt) is how forces transfer momentum. The impulse-momentum theorem says J = Δp. This is why crumple zones in cars and bending knees when landing both protect you: they EXTEND the time over which momentum changes, which REDUCES the average force.
3. Momentum is always conserved; kinetic energy isn't
In every collision, momentum is conserved (assuming no net external force). Kinetic energy is conserved ONLY in elastic collisions. Most real-world collisions are inelastic — some KE becomes heat, sound, or deformation energy. In a perfectly inelastic collision, the objects stick together, and the MOST KE is lost (but momentum is still conserved).