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Ice-skater spin
Beginner
Pulling arms in reduces I and increases ω.
Pulling her arms in lowers I, so ω must increase to keep Iω constant. Kinetic energy increases because the skater does work pulling inward.
I from 4 to 1.5 kg·m² turns 2 rev/s into 5.3 rev/s.
Angular momentum is conserved, kinetic energy is not.
In more detail
A skater spinning with arms outstretched has a larger moment of inertia. Pulling the arms in reduces it, and angular momentum conservation makes the spin rate increase.
Real-world uses
- Figure skating spins and pirouettes use this effect to speed up.
- Divers tuck to increase their rotation speed.
- A skater starting a spin with arms out and then pulling them in can spin many times faster without any push.
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Frequently asked questions
Why does the spin speed up?
Because the moment of inertia decreases, so the angular velocity must increase to keep L constant.
Where does the extra energy come from?
From the skater's muscles doing work to pull the arms in.
Where does the extra kinetic energy come from?
The skater does work by pulling the arms inward against the increasing centrifugal effect, which raises the rotational energy.
Related topics in Momentum & Collisions
Jet and conveyor problems · Angular momentum · Conservation of angular momentum · Kepler's second law from L · Collision of particles in physics labs · Compton scattering