What it does
A spinning body keeps its angular momentum L = I ω as long as nothing twists it from outside. The moment of inertia I depends on where the mass is: the further from the axis, the bigger I. So when a skater pulls her arms in, I falls, and ω must rise to keep L the same.
The kinetic energy is ½ I ω², which equals L² ÷ 2I. With L fixed and I smaller, the energy goes up. It comes from the work her muscles do pulling the arms inwards against the “pull outwards” you feel when spinning. This is a teaching model, not a real skater. To find where the mass is balanced first, see centre of mass, and for rotation with moving along a surface see rolling race.
How to use it
- Set the weight in each hand and the starting spin.
- Press Pull arms in (or move the r slider yourself) and watch ω, I, L and the kinetic energy.
- Arms out takes them back; Pause freezes the picture.
What each setting does
- Hands from the axis r: how far the weights are from the middle.
- Spin with arms out ω₀: the speed when r = 1 m.
- Weight in each hand: more weight means arms matter more.
Worked example
Leave the starting spin at 2 rad/s and the weights at 2 kg. With arms out, I = 1 + 2 × 2 × 1² = 5 kg m², so L = 5 × 2 = 10 kg m²/s and the kinetic energy is ½ × 5 × 2² = 10 J.
Pull the hands in to r = 0.5 m. Now I = 1 + 2 × 2 × 0.5² = 2 kg m². L is still 10, so ω = 10 ÷ 2 = 5 rad/s, and the kinetic energy is ½ × 2 × 5² = 25 J.
FAQs
Where does the extra energy come from? From the skater: her muscles do work moving the weights inwards.
Is the angular momentum really constant? Yes, in this model there is no friction or outside twist, so L cannot change.
What if the weights are zero? Then the arms hardly matter in the model, so I stays 1 kg m² and nothing changes.
Is anything stored? No. Everything is worked out in your browser.
Where the numbers come from
- Conservation of angular momentum, I = ΣmR² and rotational kinetic energy ½Iω²: standard Class 11 physics (system of particles and rotational motion). The skater is fibub's own teaching model: a body of I = 1 kg m² holding two weights.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Read more on the Blog
- Angular momentum: why a spinning skater speeds up(the full guide)
Last updated 2026-11-10.