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.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
The gymnast’s angular momentum L is conserved because no external torque acts.
1. When the body is tucked the moment of inertia I is small.
2. Extending the limbs moves mass further from the axis, so I increases.
3. With L constant, ω = L/I decreases – the gymnast rotates more slowly when extended.
4. Rotational kinetic energy E = L²/(2I). A larger I gives a smaller E, so the kinetic energy is lower after extending.
5. The ‘lost’ energy is dissipated as internal (thermal/chemical) energy in the muscles doing negative work against the centrifugal effect.
1. When the body is tucked the moment of inertia I is small.
2. Extending the limbs moves mass further from the axis, so I increases.
3. With L constant, ω = L/I decreases – the gymnast rotates more slowly when extended.
4. Rotational kinetic energy E = L²/(2I). A larger I gives a smaller E, so the kinetic energy is lower after extending.
5. The ‘lost’ energy is dissipated as internal (thermal/chemical) energy in the muscles doing negative work against the centrifugal effect.
Examiner tips
- Show the conservation of angular momentum first; link I increase to ω decrease. Include the formula E = L²/(2I) to justify the energy change. Explain the internal energy conversion briefly.
- common_mistakes
- :
- Forgetting that L is conserved. Using the wrong relationship between I and ω (e.g. ω∝I). Not mentioning the internal energy conversion or using the wrong energy expression.
Mark scheme (4 marks)
- In the absence of external torque, the angular momentum of the gymnast is conserved throughout the somersault.
- Extending the body moves mass further from the axis of rotation, increasing the moment of inertia.
- Since L = Iω is constant, a larger moment of inertia requires a smaller angular velocity, so the gymnast rotates more slowly when extended.
- 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.
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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