# Motion in a circle

> CIE A-Level Physics · CIE 9702
> Source: https://www.owlsprep.com/study/cie-9702-u16-overview/
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This unit introduces core concepts of uniform circular motion, connects linear kinematics to rotational motion, and equips you to analyze common circular motion scenarios tested in CIE A-Level Physics.

**Prerequisites:** Linear kinematics and Newton's laws of motion; Basic right-angle trigonometry

## Learning objectives

- Describe uniform circular motion using angular quantities and convert between angular and linear motion variables
- Derive and apply standard formulas for centripetal acceleration
- Analyze forces on objects in circular motion and solve problems for real-world scenarios

## Unit at a glance

This unit builds on your existing knowledge of linear motion to describe motion along a circular path. We start by defining new rotational quantities that simplify describing circular motion, before moving to the key insight that uniform circular motion requires constant acceleration directed towards the center of the circle.

Topics build sequentially: you will first learn how to describe how fast an object rotates, then calculate its acceleration, then find the net force required to keep it moving in a circular path. This sequence mirrors how you learned linear motion earlier in your course.

Core sub-topics in this unit:
- [Angular displacement and speed](https://www.owlsprep.com/study/cie-9702-u16-angular-displacement-and-speed/) — Learn to define angular quantities and convert between angular and linear speed for circular motion.
- [Centripetal acceleration](https://www.owlsprep.com/study/cie-9702-u16-centripetal-acceleration/) — Derive the formula for centripetal acceleration and understand its constant inward direction.
- [Centripetal force](https://www.owlsprep.com/study/cie-9702-u16-centripetal-force/) — Apply Newton's second law to solve problems involving centripetal force in real contexts.

## Common pitfalls

- **Wrong:** Treating centripetal force as a new, separate force that acts in addition to existing forces on the object.
  - Why it fails: This leads to incorrect free-body diagrams and wrong calculations for net force.
  - Correct: Remember centripetal force is the net inward force from existing forces (tension, friction, gravity etc.), not an extra force.
- **Wrong:** Adding an outward 'centrifugal' force to force diagrams for circular motion.
  - Why it fails: This fictitious force only appears in non-inertial reference frames and is not required for CIE A-Level problems.
  - Correct: All analysis is done from an inertial frame, so only a net inward centripetal force is included.

## Cheatsheet

| Concept | Key Formula |
| --- | --- |
| Angular displacement | $\theta = \frac{s}{r}$ (units: radians) |
| Angular speed | $\omega = \frac{\Delta\theta}{\Delta t} = 2\pi f$ |
| Linear-angular speed relation | $v = r\omega$ |
| Centripetal acceleration | $a_c = \frac{v^2}{r} = r\omega^2$ |
| Centripetal force | $F_c = \frac{mv^2}{r} = mr\omega^2$ |

## What's next

Begin your study of this unit with the first sub-topic on angular displacement and speed, where you will learn the foundational rotational quantities needed for all subsequent topics in this unit. Once you complete all three sub-topics here, you can move on to the next unit on gravitational fields, which builds on circular motion concepts to analyze planetary orbits.

- [Angular displacement and speed](https://www.owlsprep.com/study/cie-9702-u16-angular-displacement-and-speed/)
- [Gravitational fields](https://www.owlsprep.com/study/cie-9702-u17-overview/)
- [Centripetal acceleration](https://www.owlsprep.com/study/cie-9702-u16-centripetal-acceleration/)

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