January 17, 2026

AP Physics 1: Conservation of Momentum

3D illustration of Newton's Cradle showing momentum transfer from one ball to another.

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AP Physics 1: Conservation of Momentum

If you master one concept in Unit 5, make it this one. The Law of Conservation of Momentum is one of the most fundamental laws in the universe. It applies to everything from billiard balls to subatomic particles to colliding galaxies.

AP Physics 1 Unit 5 (Topics 5.3–5.4): One-dimensional and two-dimensional collisions, conservation of momentum in closed systems, and classifying elastic vs inelastic collisions.

1. The Law (p_i = p_f)

The law states: If there are no external forces acting on a system (like friction), the total momentum of that system remains constant.

    \[\sum \vec{p}_i = \sum \vec{p}_f\]

Total Initial Momentum = Total Final Momentum

For a collision between two objects (A and B), the equation looks like this:

    \[m_A v_{Ai} + m_B v_{Bi} = m_A v_{Af} + m_B v_{Bf}\]

This is your starting point for almost every collision problem.

2. Types of Collisions

Not all collisions are the same. In AP Physics, we classify them based on what happens to the Kinetic Energy (K).

Diagram comparing Elastic (bouncing), Inelastic (sticking), and Explosion scenarios.

Collision Types: Elastic collisions conserve Kinetic Energy. Inelastic collisions lose Kinetic Energy (usually to heat or deformation).

The Cheat Sheet:

  • Elastic Collision: Objects bounce perfectly. Momentum is conserved. Kinetic Energy IS conserved. (Rare in real life, common with atoms/magnets).
  • Inelastic Collision: Objects bounce or deform. Momentum is conserved. Kinetic Energy is LOST. (Most real-world car crashes).
  • Perfectly Inelastic: Objects stick together. Momentum is conserved. Maximum possible kinetic energy is lost.
  • Explosion (Recoil): Objects start together (v_i = 0) and push apart. Momentum is conserved (total = 0). Energy is gained from chemical or spring potential.
⚠️ Exam Tip: Never assume a collision is elastic unless the problem explicitly tells you it is. Always assume inelastic (energy lost) by default.

3. 2D Collisions (Glancing Blows)

Momentum is a vector. This means if objects collide at an angle, you must conserve momentum in the x-direction and the y-direction separately.

Diagram of a glancing collision showing momentum vectors resolving into X and Y components.

2D Collisions: Momentum is conserved in the x-direction and y-direction independently.

Step-by-Step Strategy:

  1. X-axis equation: Sum of momentum before (x) = sum of momentum after (x).
  2. Y-axis equation: Sum of momentum before (y) = sum of momentum after (y).
  3. Resolve vectors: Use \cos \theta for horizontal and \sin \theta for vertical components.

4. Quick AP Practice

📚 AP Practice Problems

1. A 1 kg cart moving at 3 m/s hits a 2 kg cart at rest and they stick. Final speed?

Answer v_f = \frac{(1)(3) + (2)(0)}{1+2} = 1 \text{ m/s}

2. Two equal-mass carts collide elastically head‑on with speeds 2 m/s and −3 m/s. What are their speeds after?

Answer They exchange speeds: v_{1f} = -3 \text{ m/s},\ v_{2f} = 2 \text{ m/s}.

3. An explosion breaks a 3 kg object at rest into 1 kg and 2 kg pieces. The 1 kg piece moves right at 6 m/s. Find the 2 kg piece’s velocity.

Answer Total p_i = 0. So 0 = (1)(6) + (2)v_2 \Rightarrow v_2 = -3 \text{ m/s} (left).

Unit 5 Complete!

You have mastered Momentum, Impulse, and Collisions. Next, we move to Simple Harmonic Motion (SHM)—the physics of pendulums and springs.

Next Unit: Simple Harmonic Motion (Unit 6) →