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Physics 1 · 16 min read · Updated 2026-05-11

AP Physics 1: Linear Momentum — AP Physics 1

AP Physics 1 · AP Physics 1 CED (2024-25) · 16 min read

1. Linear Momentum and the Impulse-Momentum Theorem ★★☆☆☆ ⏱ 4 min

Momentum accounts for 10-15% of your total AP Physics 1 exam score. Because it depends on velocity (a vector) not speed, an object moving in a circle at constant speed has constantly changing momentum, even though its speed is constant.

\vec{p} = m\vec{v}

Exam tip: Free-response questions often ask you to explain safety features like airbags: increasing contact time $\Delta t$ for a fixed change in momentum reduces average force, lowering injury risk.

2. Conservation of Momentum in 1D and 2D Collisions ★★★☆☆ ⏱ 5 min

Momentum is conserved for any closed, isolated system: a system with no net external force acting on it, and no mass entering or leaving. For collisions between objects, internal forces are equal and opposite (Newton's third law) so they cancel out, leaving total system momentum unchanged.

\sum \vec{p}_{initial} = \sum \vec{p}_{final}

For 1D collisions, you only need to track sign to account for direction. For 2D collisions, momentum is conserved separately for the x and y components of motion, since perpendicular vector components do not affect each other.

3. Elastic vs Inelastic Collisions ★★☆☆☆ ⏱ 3 min

While momentum is conserved for all isolated collisions, kinetic energy (KE) is only conserved for a small subset of collisions, leading to three standard classifications:

  • **Elastic collision**: Both momentum and kinetic energy are conserved. No permanent deformation occurs, and no energy is lost to heat, sound, or internal friction. Only approximated in macroscopic interactions like billiard ball collisions.
  • **Inelastic collision**: Momentum is conserved, but kinetic energy is not. Some kinetic energy is converted to other forms. Most real-world collisions fall into this category.
  • **Perfectly inelastic collision**: A special case of inelastic collision where colliding objects stick together after impact, resulting in the maximum possible loss of kinetic energy.

4. Center of Mass ★★★☆☆ ⏱ 4 min

For a 1D system of particles, the center of mass position is calculated with the formula below. Center of mass velocity follows the same proportional structure: $v_{cm} = \frac{\sum m_i v_i}{M_{total}} = \frac{p_{total}}{M_{total}}$, so constant total momentum means constant COM velocity.

x_{cm} = \frac{m_1x_1 + m_2x_2 + ... + m_nx_n}{M_{total}}

Common Pitfalls

Why: Students confuse momentum with kinetic energy, which is a scalar.

Why: Students forget the requirement of a closed, isolated system for momentum conservation.

Why: Students mix up momentum conservation (always true for isolated systems) with kinetic energy conservation (only true for elastic collisions).

Why: Students skip setting up a coordinate system to save time.

Why: Students forget that Newton's third law applies to collision forces between objects.

Quick Reference Cheatsheet

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