# Circular motion and simple harmonic motion

> Angular velocity, centripetal acceleration and force, the conditions for SHM, displacement/velocity/acceleration relationships, energy in SHM, damping and resonance.

Canonical: https://revise-gray.vercel.app/library?topic=wjec-alevel-physics.circular-shm
Last updated: 2026-08-01

Flagship subject: topics and specification statements are authored to the WJEC specification. No question in it has been through human review yet.

- Subject: [WJEC · A Level · Physics](https://revise-gray.vercel.app/library?subject=wjec-alevel-physics)
- Specification reference: Unit 3.2–3.3
- Difficulty: 4/5
- Assessment objectives: AO1, AO2
- Status: authored · checked · 2026-08-01

## Specification coverage

| Reference | Statement | AOs |
| --- | --- | --- |
| Unit 3.2(a) | define angular velocity and relate linear and angular speed by v equals omega r | AO1 |
| Unit 3.2(b) | derive and apply centripetal acceleration a equals v squared over r equals omega squared r | AO2 |
| Unit 3.2(c) | state the defining condition for simple harmonic motion a equals minus omega squared x | AO1 |
| Unit 3.2(d) | relate displacement velocity and acceleration in SHM and determine period from omega | AO2 |
| Unit 3.2(e) | calculate period of a simple pendulum and a mass-spring system | AO2 |
| Unit 3.2(f) | describe energy interchange between kinetic and potential during SHM | AO1, AO2 |
| Unit 3.2(g) | explain damping and resonance including effect on amplitude-frequency response | AO1, AO2 |

## Summary

Angular velocity, centripetal acceleration and force, the conditions for SHM, displacement/velocity/acceleration relationships, energy in SHM, damping and resonance.

## What earns marks

- a = v²/r = ω²r, directed toward the centre; the centripetal force is provided by a real force, not an extra one.
- SHM requires a = −ω²x: acceleration proportional to displacement and directed toward equilibrium.
- T = 2π√(l/g) for a simple pendulum; T = 2π√(m/k) for a mass–spring system.
- Resonance occurs when the driving frequency equals the natural frequency; damping reduces and broadens the peak.

## Where marks are lost

- Adding 'centripetal force' to a free-body diagram as if it were a separate force.
- Losing the minus sign in a = −ω²x and so the direction of acceleration.
- Using degrees for ω in radian-based formulae.

## Related

- [WJEC · A Level · Physics](https://revise-gray.vercel.app/library?subject=wjec-alevel-physics)
- [Circular motion and simple harmonic motion lesson](https://revise-gray.vercel.app/lesson?subject=wjec-alevel-physics&topic=wjec-alevel-physics.circular-shm)