Explore the Conservation of Angular Momentum: Spinning
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.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Conservation of Angular Momentum: Spinning with sample data entered and the result showing.
What is the Conservation of Angular Momentum: Spinning?
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. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
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.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
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.
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.
Used for
Pick one to see how it fits.
Physics learners
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.
Try it freeTeachers
For teachers: project the Conservation of Angular Momentum: Spinning Disks & Skater Lab on the board, let students predict the result, then run it together and test this: Drop a fast disk onto a much heavier stationary one and see how little it speeds the second one up. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
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. The Conservation of Angular Momentum: Spinning Disks & Skater Lab is free, needs no signup or download and runs in your web browser. It is part of the Physics group of AZRS simulations.
Does the Conservation of Angular Momentum: Spinning Disks & Skater Lab work on a phone or tablet?
Yes. The Conservation of Angular Momentum: Spinning Disks & Skater Lab takes touch input as well as mouse input, so you can use its 4 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Conservation of Angular Momentum: Spinning?
1. In 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. 2. In the Conservation of Angular Momentum: Spinning Disks & Skater Lab, pick an option such as Spinning skater, Merging disks to switch modes or load an example. 3. Start with this experiment: Pull the skater's arms all the way in and watch her spin rate climb. Drag any glowing handle, object or slider with your mouse or finger and the Conservation of Angular Momentum: Spinning Disks & Skater Lab responds in real time. 4. Change one setting at a time and watch which readout moves, then compare it with this idea: Angular momentum L = Iω is conserved whenever no external torque acts on a system, even as the moment of inertia I changes shape.
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Pull a spinning skater's arms in and watch her spin speed up exactly as L = Iω is. Free to use.
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