Conservation of Momentum
Lesson notes
Overview
In any collision the total momentum before equals the total after. This topic is rated beginner and is number 18 of 227 in Physics. Core ideas and first intuitions. No prior knowledge needed.
What you are seeing
The panel above shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
Momentum p = mv is conserved whenever there is no external force on a system. In a collision the total momentum before equals the total after, m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′, even if energy is lost. It is a vector, so each direction is conserved separately. This law explains recoil of a gun, the motion of rockets, and the outcomes of collisions in particle physics and car crashes.
Reading the relationship
The expression "m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′" is a compact summary of the idea. It uses the symbols m₁v, m₂v; name what each one stands for before you start. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Run the animation once with the default settings and describe in words what happens. 2. Change one slider at a time and note which quantity responds most. 3. Push each slider to its extreme and decide whether the result still makes sense.
Try this
Start by only moving one slider at a time. Say aloud what you expect, then check.
Common pitfalls
Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.
How it connects
It builds on “Pulleys and the Atwood Machine”, the topic before it in Physics. Once you are comfortable, continue with “Elastic Collisions”.
Why it matters
Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.
Where you might use it
- Revising “Conservation of Momentum” before a class, exam or certification
- Designing vehicles, bridges and devices where motion, forces or waves must be predicted
- Understanding how sensors, lasers and communication links actually work
- Explaining everyday phenomena such as sound, light, heat and orbits
Frequently asked questions
What is Conservation of Momentum?
In any collision the total momentum before equals the total after. It is a beginner topic in Physics.
How do I use the Conservation of Momentum simulation?
The panel at the top shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′ packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Core ideas and first intuitions. No prior knowledge needed. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Pulleys and the Atwood Machine”, the previous topic in Physics. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.
Quick quiz
More in Physics
See all →Elastic Collisions
Kinetic energy is conserved as well as momentum — like billiard balls or air-track gliders.
Inelastic Collisions
Objects stick and move together; some kinetic energy turns into heat and deformation.
Impulse and Force over Time
Impulse is the area under a force–time graph and equals the change in momentum.