# Explain why a torque applied to a rigid body for a given time interval produces a greater change in angular velocity when the mass of the body is distributed close to the axis of rotation compared with when it is distributed far from the axis of rotation.

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

## Mark scheme (4 marks)

1. Torque equals the rate of change of angular momentum (τ = ΔL/Δt), so a given torque applied for a given time produces a fixed change in angular momentum ΔL.
2. Angular momentum equals the product of moment of inertia and angular velocity (L = Iω), so ΔL = IΔω.
3. When mass is distributed close to the axis, the moment of inertia I is smaller, because moment of inertia depends on mr² and r is smaller for each mass element.
4. Since ΔL is fixed and I is smaller, Δω = ΔL/I must be larger, so the body gains a greater change in angular velocity.

## Key terms

- [torque](https://www.gradenine.co.uk/glossary/torque)
- [angular velocity](https://www.gradenine.co.uk/glossary/angular-velocity)
- [axis of rotation](https://www.gradenine.co.uk/glossary/axis-of-rotation)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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