Conservation of Angular Momentum: Spinning Disks & Skater Lab
Pull a spinning skater's arms in and watch her spin speed up exactly as L = Iω is conserved, or drop one spinning disk onto another and see them lock together.
Pull the skater's arms in and watch her spin faster - angular momentum stays constant while her moment of inertia drops. Then try dropping a spinning disk onto a stationary one and see them lock together.
About the Conservation of Angular Momentum: Spinning Disks & Skater Lab
Free conservation of angular momentum: spinning disks & skater lab. Pull a spinning skater's arms in and watch her spin speed up exactly as L = Iω is conserved, or drop one spinning disk onto another and see them lock together. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for physics, the conservation of angular momentum: spinning disks & skater lab runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Pull a spinning skater's arms in and watch her spin speed up exactly as L = Iω is conserved, or drop one spinning disk onto another and see them lock together. Use it to explore physics ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Conservation of Angular Momentum: Spinning Disks & Skater Lab
- Use the controls to change Scene, Arm extension (m from axis), Initial spin ω₁, Second disk moment of inertia I₂. The simulation reacts instantly.
- Pick an option such as Spinning skater, Merging disks to switch modes or load an example.
- Press "Reset to defaults", "Lab Report" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Pull the skater's arms all the way in and watch her spin rate climb.
- Drop a fast disk onto a much heavier stationary one and see how little it speeds the second one up.
- Try the final-spin-rate challenge for the skater.
- Compute the percent kinetic energy lost in the merging-disks challenge.
Key ideas you can learn
- Angular momentum L = Iω is conserved whenever no external torque acts on a system, even as the moment of inertia I changes shape.
- Pulling mass closer to the rotation axis reduces moment of inertia; since L stays constant, angular speed ω must increase to compensate - the ice-skater effect.
- When one spinning object merges with a stationary one (a perfectly inelastic angular collision), angular momentum is conserved but rotational kinetic energy is not - some is lost to the internal forces that lock them together.
- The kinetic energy lost fraction in a merging-disk collision depends only on the ratio of the two moments of inertia, not on the spin speed.
Show my work
Challenges
Challenge 1 - skater's final spin rate
In the skater scene, note her starting arm extension and ω₁. Now imagine pulling her arms all the way to 0.3 m. Using I ∝ r² for a point mass approximation and L = Iω conserved, compute her new angular speed ω₂ = ω₁(r₁/r₂)². Enter ω₂ in rad/s.
Challenge 2 - kinetic energy lost in merging disks
Switch to the merging-disks scene. A disk with I₁ = 1.0 kg·m² spins at ω₁ = 10 rad/s and drops onto a stationary disk with the I₂ you set. They stick together (inelastic). Compute the percent of kinetic energy lost: %lost = 100 × (1 − I₁/(I₁+I₂)). Enter the percentage.
Where this is used in the real world
Figure skaters and divers use exactly this pull-in-to-spin-faster technique, and engineers analyze coupling clutches and docking spacecraft with the same conservation-of-angular-momentum plus energy-loss reasoning.
Who is this simulation for?
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams. It works well for flipped classrooms because students can explore before the lesson.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
Why does a skater spin faster when she pulls her arms in?
Pulling her arms in reduces her moment of inertia I because mass moves closer to the rotation axis, and since angular momentum L = Iω must stay constant with no external torque, a smaller I forces a larger ω.
Why is kinetic energy lost when two spinning disks merge, if angular momentum is conserved?
Angular momentum conservation only requires no net external torque, but the internal friction and deformation that lock the two disks together do negative work on the system, converting some rotational kinetic energy into heat and sound, just like a perfectly inelastic linear collision.
Is the Conservation of Angular Momentum: Spinning Disks & Skater Lab free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Conservation of Angular Momentum: Spinning Disks & Skater Lab work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.