# A gymnast performs a somersault by tucking their body into a compact ball shape during the rotation and then extending fully before landing. Explain why the gymnast rotates more slowly when fully extended compared to when tucked, and explain why the total mechanical energy of the gymnast is less after extending than when tucked, even though no external torque acts during the somersault.

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

## Mark scheme (4 marks)

1. In the absence of external torque, the angular momentum of the gymnast is conserved throughout the somersault.
2. Extending the body moves mass further from the axis of rotation, increasing the moment of inertia.
3. Since L = Iω is constant, a larger moment of inertia requires a smaller angular velocity, so the gymnast rotates more slowly when extended.
4. Rotational kinetic energy is E = L²/(2I); with L constant, a larger I gives a smaller kinetic energy, so energy decreases when the gymnast extends. The 'lost' energy is converted to internal (thermal/chemical) energy in the muscles doing negative work to extend the body against centrifugal effects.

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