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Momentum & Collisions · Physics

Conservation of Linear Momentum

When net external impulse is zero, total momentum stays constant: \(\Delta \vec P = \vec 0\).

This topic includes

Subtopics to master

Learn the conditions, choose the right system, and apply conservation in 1D and 2D.

When it works
Conditions for Momentum Conservation
Momentum is conserved when net external impulse over the interaction is zero (or negligible).
  • External impulse test
  • Short-time collisions
  • What “negligible” means
Start subtopicRule of thumb.
System choice
Isolated Systems
An isolated system experiences no net external force (or no external impulse).
  • System boundaries
  • External forces vs impulses
  • Real approximations
Start subtopicPick smart boundaries.
Forces
Internal vs External Forces
Internal forces come in equal-and-opposite pairs and do not change total system momentum.
  • Internal cancellation
  • External impulses change \(\vec P\)
  • Common mistakes
Start subtopicKey reasoning step.
1D
Momentum Conservation in 1D
Solve head-on interactions with one scalar equation (with signs).
  • Before = after
  • Sign conventions
  • Two-body setups
Start subtopicFast solving.
2D
Momentum Conservation in 2D
Use vector components: conserve \(p_x\) and \(p_y\) separately.
  • Component equations
  • Angles and vectors
  • Scattering setups
Start subtopicVector mastery.
Practice
Practice & Exercises
Become fluent applying conservation quickly and correctly.
  • System-boundary selection drills
  • 1D conservation problem sets
  • 2D component problems
  • Impulse/external force checks
  • Concept quizzes (what is conserved?)
Open practiceConfidence builder.