Unit Overview

Motion in a circle

CIE A-Level Physics· 5 min read 📊 n/a

1. 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

Learn to define angular quantities and convert between angular and linear speed for circular motion.

★★⏱ 8 min

Centripetal acceleration

Derive the formula for centripetal acceleration and understand its constant inward direction.

★★★⏱ 10 min

Centripetal force

Apply Newton's second law to solve problems involving centripetal force in real contexts.

★★★⏱ 12 min

2. Common Pitfalls

Wrong move:

Treating centripetal force as a new, separate force that acts in addition to existing forces on the object.

Why:

This leads to incorrect free-body diagrams and wrong calculations for net force.

Correct move:

Remember centripetal force is the net inward force from existing forces (tension, friction, gravity etc.), not an extra force.

Wrong move:

Adding an outward 'centrifugal' force to force diagrams for circular motion.

Why:

This fictitious force only appears in non-inertial reference frames and is not required for CIE A-Level problems.

Correct move:

All analysis is done from an inertial frame, so only a net inward centripetal force is included.

3. Quick Reference Cheatsheet

Concept	Key Formula
Angular displacement	$θ = \frac{s}{r}$ (units: radians)
Angular speed	$ω = \frac{Δ θ}{Δ t} = 2 π f$
Linear-angular speed relation	$v = r ω$
Centripetal acceleration	$a_{c} = \frac{v ^{2}}{r} = r ω^{2}$
Centripetal force	$F_{c} = \frac{m v ^{2}}{r} = m r ω^{2}$

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.