Conservation of Angular Momentum: Spinning Disks & Skater Lab Community
Questions, answers and tips from people who use the 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..
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From the tool guide: common questions about Conservation of Angular Momentum: Spinning Disks & Skater Lab
The items below are not posts by community members. They come from the written guide for this tool and are here to get a conversation started. Use “Ask a follow-up” to open a thread about any of them.
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.
From the tool guide Ask a follow-upWhy 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.
From the tool guide Ask a follow-upKey ideas
- 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.
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.
Where this is used
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.
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