Explain why a spinning ice skater rotates faster when they pull their arms close to their body, and outline what happens to the skater's rotational kinetic energy during this process.

IB DP Physics Higher Level (2023 syllabus) — A.4 Rigid body mechanics (HL only) · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

An ice skater begins a spin with arms extended outward. They then pull their arms tightly against their body, causing their rate of spin to increase noticeably.

Model answer (4 marks)

No external torque acts on the skater, so angular momentum L is conserved.

When the skater pulls the arms in, the mass is redistributed closer to the axis, reducing the moment of inertia I.

Because L = Iω is constant and I decreases, the angular velocity ω must increase.

The rotational kinetic energy K = ½Iω² rises; the skater’s muscles do work against the centrifugal effect, so K is not conserved.

Examiner tips

  • State conservation of angular momentum first. Explain how reducing I forces ω to rise. Mention internal work increases KE. Use correct symbols (L, I, ω, K).

Common mistakes

  • Assuming external torque exists. Claiming KE is conserved. Using the wrong relationship (e.g., I∝ω instead of L=Iω).

Mark scheme (4 marks)

  1. No net external torque acts on the skater (friction at the blade contact point is negligible), so angular momentum is conserved.
  2. Pulling arms inward reduces the skater's moment of inertia (mass is redistributed closer to the rotation axis).
  3. Because L = Iω is conserved and I decreases, the angular velocity ω must increase.
  4. The rotational kinetic energy increases because the skater does work (uses internal/muscular energy) pulling their arms inward against the centrifugal effect, so rotational KE is not conserved.

Key terms in this question

rotational kinetic energy

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