Pulleys and the Atwood Machine
Lesson notes
Overview
Two masses over a pulley accelerate at (m₂−m₁)g/(m₁+m₂). This topic is rated beginner and is number 17 of 227 in Physics. Core ideas and first intuitions. No prior knowledge needed.
What you are seeing
The panel above shows objects with force arrows, so you can see how the net force changes the motion. 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
In an Atwood machine two masses hang over an ideal pulley. The heavier one descends, and both share the same acceleration a = (m₂ − m₁)g/(m₁ + m₂), always less than g. Applying Newton’s second law to each mass gives the string tension T = 2m₁m₂g/(m₁ + m₂). When the masses are equal nothing accelerates. Real pulleys have mass and friction, which reduce the acceleration, and pulley systems are used to gain mechanical advantage.
Reading the relationship
The expression "a = (m₂ − m₁)g/(m₁ + m₂)" is a compact summary of the idea. It uses the symbols a, m₂, m₁, g; name what each one stands for before you start. Notice that it contains a ratio, so increasing the denominator makes the result smaller. 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 “Torque and Levers”, the topic before it in Physics. Once you are comfortable, continue with “Conservation of Momentum”.
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 “Pulleys and the Atwood Machine” 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 Pulleys and the Atwood Machine?
Two masses over a pulley accelerate at (m₂−m₁)g/(m₁+m₂). It is a beginner topic in Physics.
How do I use the Pulleys and the Atwood Machine simulation?
The panel at the top shows objects with force arrows, so you can see how the net force changes the motion. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression a = (m₂ − m₁)g/(m₁ + m₂) 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 “Torque and Levers”, 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 →Conservation of Momentum
In any collision the total momentum before equals the total after.
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.