Where can I learn Kinematics of uniform circular motion for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 12.1 (Kinematics of uniform circular motion) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/12-1-kinematics-of-uniform-circular-motion.

Is Kinematics of uniform circular motion (12.1) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Kinematics of uniform circular motion.

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12.1Physics25 min readPREMIUM

Kinematics of uniform circular motion

Welcome to the exciting world of uniform circular motion! Ever wondered how roller coasters loop-the-loop or satellites stay in orbit? It all comes down to the physics of objects moving in circles. We'll explore key concepts like angular displacement, angular velocity, centripetal acceleration, and centripetal force that govern this fundamental type of movement. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 12.1.

BY THE END, YOU CAN…

exam checklist — tick these off

1Define and use angular displacement, angular velocity, period, and frequency.
2Explain and calculate centripetal acceleration and centripetal force.
3Identify the source of centripetal force in various physical situations.
4Solve problems involving uniform circular motion using relevant formulas.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Kinematics of uniform circular motion

Cambridge 9702 Paper 4 — Kinematics of uniform circular motion (12.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
12.1 Kinematics of uniform circular motion.
2
The angular displacement of a body is the change in angle (radians, degree or revolutions) through which the body rotates around a circle.
3
Angular displacement is the ratio of: 𝛥𝜃 = 𝛥𝑠 𝑟.
4
A radian (rad) is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

What this topic covers

The official Cambridge syllabus points this lesson works through.

12.1.1
Define the radian and express angular displacement in radians
12.1.2
Understand and use the concept of angular speed
12.1.3
Recall and use $ω = 2\pi /T$ and $v = rω$

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure Live interactive1 / 4

Loading simulation…

Fetching from Physics Interactives by The Physics Classroom…

Rotational Motion

Both bugs share the angular speed, and linear speed is proportional to radius.

If the embed does not load, use Open simulation.

Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

Step-synced diagram — highlights what to look for in the simulation above.

Step 1

12.1 Kinematics of uniform circular motion.

16 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

16 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

PhETStart here · 1Java · best on a laptop9702 12.1–12.2 · IB A.4 · A.1
Ladybug Revolution
Spin a turntable with a ladybug on it and read angular position, velocity and acceleration alongside the linear values.
Why this one: Read angular position, angular velocity and linear speed side by side as the turntable spins.
Try this
1. Set a steady angular velocity — the ladybug’s speed stays constant.
2. Move the ladybug outward — same ω, larger linear speed.
3. Turn on the acceleration vector — it points to the centre.
Look for v = ωr and a = ω²r: further out means faster, with acceleration always toward the axis.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
PhysicsHubStart here · 29702 12.1 · 9702 12.2 · IB A.2
Circular Motion
Object in uniform circular motion; set radius, tangential speed, mass and size and watch the velocity (tangent) and centripetal acceleration (inward) vectors
Why this one: Velocity stays tangent while acceleration points to the centre: constant speed, changing velocity.
Try this
1. Double the tangential speed and watch the acceleration vector.
2. Double the radius instead.
3. Change the mass.
Look for Acceleration points to the centre with magnitude v²/r; the velocity vector stays tangent.
Open on PhysicsHub
PhysicsHub (@mattqdev) · MIT
SimuPhysicsStart here · 39702 12.1 · IB A.2
Angle and Arc Simulation
An angle at the centre of a circle is tied to the arc it cuts, showing that arc divided by radius is the angle in radians
Why this one: Arc length divided by radius is the angle in radians, whatever the radius.
Try this
1. Set an angle and read the arc length.
2. Double the radius and read the arc again.
3. Compare arc divided by radius with the angle.
Look for Arc length divided by radius equals the angle in radians.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsStart here · 49702 12.1 · 9702 12.2 · IB A.2
Drone in a Circular Tunnel
Fly a drone around a circular tunnel and inspect velocity and acceleration vectors
Why this one: Fly a circle and compare the velocity and acceleration arrows: always perpendicular.
Try this
1. Fly the drone around the circular tunnel and watch the velocity vector.
2. Compare the direction of the acceleration vector with the velocity vector.
Look for Velocity is tangential while acceleration points to the centre, perpendicular to it.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
The Physics ClassroomStart here · 59702 12.1 · 9702 12.2 · IB A.2
Uniform Circular Motion
Change the mass, speed or radius and see the velocity, acceleration and net force on an object moving in a circle
Why this one: Double the speed and the acceleration quadruples; double the radius and it halves.
Try this
1. Double the speed and read the acceleration.
2. Double the radius and compare.
3. Change the mass and compare the net force.
Look for Centripetal acceleration equals v² divided by r.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

More simulations11 more on this topic — core ones first

PhETCoreJava · best on a laptop9702 12.1–12.2 · 1.4 · IB A.1
Motion in 2D
Drag an object, or pick circular or elliptical motion, and watch the velocity and acceleration vectors.
Try this
1. Choose circular motion — velocity is tangential and acceleration points inward.
2. Choose elliptical — the acceleration no longer points at the centre.
3. Drag freely — speed up and watch the acceleration arrow swing forward.
Look for Uniform circular motion has constant speed but an acceleration toward the centre: v²/r.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
oPhysicsCore9702 12.1 · 9702 12.2 · IB A.2
The Conical Pendulum
Conical pendulum: adjust radius and view; see tension and weight resolving to give centripetal force
Try this
1. Increase the radius and watch the tension vector.
2. Change the view to look at the forces from the side.
3. Reduce the radius until the string hangs nearly vertical.
Look for The vertical component of tension balances the weight; the horizontal component supplies the centripetal force.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsCore9702 12.1 · 9702 12.2 · IB A.2
Circular Motion Simulation
The velocity and acceleration vectors are drawn as an object circles at steady speed
Try this
1. Watch the velocity vector round the circle.
2. Watch the acceleration vector.
3. Change the speed and compare the acceleration.
Look for Velocity is tangent to the circle and acceleration points towards the centre.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsCore9702 12.1 · 9702 12.2 · 9702 3.1
A Disk on a Turntable
Spin a turntable with a disk on it; find the speed at which friction can no longer hold it
Try this
1. Spin the turntable slowly and watch the disk stay put.
2. Raise the speed until the disk slides off; note the speed.
Look for Friction supplies the centripetal force until mv²/r exceeds the maximum friction, at which point the disk slips.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 12.1 · 9702 12.2 · IB A.2
Car on a Banked Road Problem 1
Drive a car on a banked curve; find the speed at which no friction is needed (banked up)
Try this
1. Drive the car around the banked curve and find the speed needing no friction.
2. Compare that speed with the banking angle.
Look for With no friction the horizontal component of the normal force alone supplies mv²/r, fixing one speed per banking angle.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 12.1 · 9702 12.2 · IB A.2
Car on a Banked Road Problem 2
Second banked-road case with the friction direction reversed
Try this
1. Drive the car around the curve and note the direction of friction.
2. Compare the speed with the no-friction case from Problem 1.
Look for Below the no-friction speed, friction acts up the slope to stop the car sliding down.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$1\text{ rad} = \frac{180^\circ}{\pi} \approx 57.3^\circ$

KEY RELATION

$f = \frac{1}{T}$

Tap a symbol — great for exam definitions

KEY RELATION

$\omega = \frac{\Delta\theta}{\Delta t} = \frac{2\pi}{T} = 2\pi f$

Tap a symbol — great for exam definitions

KEY RELATION

$v = \omega r$

Tap a symbol — great for exam definitions

KEY RELATION

$a_c = \frac{v^2}{r} = \omega^2 r$

Tap a symbol — great for exam definitions

KEY RELATION

$F_c = ma_c = \frac{mv^2}{r} = m\omega^2 r$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

What is Uniform Circular Motion?

Uniform circular motion describes an object tracing a circular path while maintaining a constant speed. Crucially, even though its speed doesn't change, its direction is continuously changing. Because velocity is a vector (it has both magnitude and direction), a change in direction means the object's velocity is constantly changing. This continuous change in velocity implies that the object must be accelerating.

Not clear?

Angular Displacement ($\theta$) and the Radian

When an object moves in a circle, we can describe its position using the angle it has swept out from the center. This is called angular displacement ( $\theta$ ). Instead of degrees, physicists often use a unit called the radian (rad) for angular measurements in circular motion.

$1\text{ rad} = \frac{180^\circ}{\pi} \approx 57.3^\circ$

12.1 Kinematics of uniform circular motion.
The angular displacement of a body is the change in angle (radians, degree or revolutions) through which the body rotates around a circle.
Angular displacement is the ratio of: 𝛥𝜃 = 𝛥𝑠 𝑟.
A radian (rad) is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
Radians is usually written in term of π.
For a rotation for a complete circle (360 0 ), the radians is 2 π ( 𝛥𝜃 = 2πr/r).

Not clear?

Period ($T$) and Frequency ($f$)

These terms help us describe how fast an object completes its circular path. The period ( $T$ ) is simply the time taken for one complete revolution around the circle, measured in seconds. The frequency ( $f$ ) is the number of revolutions completed per unit time, usually per second. They are intimately linked.

$f = \frac{1}{T}$

Not clear?

Angular Velocity ($\omega$)

Just as linear velocity measures the rate of change of linear displacement, angular velocity ( $\omega$ ) measures the rate of change of angular displacement. Its standard unit is radians per second (rad s⁻¹). Its direction is typically described as clockwise or anticlockwise.

$\omega = \frac{\Delta\theta}{\Delta t} = \frac{2\pi}{T} = 2\pi f$

Not clear?

Linking Linear and Angular Speed

The linear speed ( $v$ ) of an object moving in a circle, which is tangent to the path, is directly related to its angular velocity ( $\omega$ ) and the radius ( $r$ ) of the circular path. A larger radius or faster angular spin results in a greater linear speed.

$v = \omega r$

Not clear?

Acceleration in Circular Motion

This is a key concept! Even if an object is moving at a constant speed in a circle, its velocity is continuously changing because its direction is constantly turning. Since acceleration is defined as the rate of change of velocity, an object in uniform circular motion is always accelerating.

Velocity is a vector quantity (magnitude and direction).
Constant speed means constant magnitude of velocity.
Changing direction means changing vector velocity.
A changing velocity means there is an acceleration.

Not clear?

Centripetal Acceleration ($a_c$)

The acceleration an object experiences in uniform circular motion is called centripetal acceleration ( $a_c$ ). The word 'centripetal' means 'centre-seeking'. This acceleration is always directed towards the exact center of the circular path, acting perpendicular to the object's instantaneous linear velocity.

$a_c = \frac{v^2}{r} = \omega^2 r$

Not clear?

Centripetal Force ($F_c$)

According to Newton's Second Law, if an object is accelerating, there must be a resultant force acting on it. This force, which is necessary to maintain circular motion, is called centripetal force ( $F_c$ ). Like centripetal acceleration, it is always directed towards the center of the circle, perpendicular to the linear velocity.

$F_c = ma_c = \frac{mv^2}{r} = m\omega^2 r$

Not clear?

Sources of Centripetal Force

It's crucial to understand that centripetal force is not a new, fundamental force of nature. It is the net force that points towards the center of the circular path. This net force is provided by one or more familiar forces.

Gravitational Force: For a planet orbiting the Sun or a satellite orbiting the Earth, the force of gravity provides the centripetal force.
Tension Force: When you swing a ball on a string, the tension in the string provides the centripetal force.
Frictional Force: For a car turning on a flat road, the static friction between the tires and the road provides the centripetal force.
Normal Force: In a loop-the-loop roller coaster, a component of the normal force from the track on the car contributes to the centripetal force.
Electric Force: For an electron orbiting a nucleus in a simple atomic model, the electrostatic attraction provides the centripetal force.

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A satellite orbits Earth in a circular path with a radius of $7.0 \times 10^6$ m and a period of $90$ minutes. Calculate its linear speed and centripetal acceleration.

1
Convert period to seconds: $T = 90 \text{ min} \times 60 \text{ s/min} = 5400 \text{ s}$ .

EXAMPLE 2

A car of mass 1200 kg travels at a constant speed of 20 m s⁻¹ around a flat, circular track of radius 50 m. Calculate (a) its angular velocity, (b) its centripetal acceleration, and (c) the minimum frictional force required between the tyres and the road to prevent it from skidding.

1
First, list the known quantities: Mass, $m = 1200$ kg Linear speed, $v = 20$ m s⁻¹ Radius, $r = 50$ m

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAKinematics of uniform circular motion

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

angular displacement: This is called angular displacement ( $\theta$ ). Instead of degrees, physicists often use a unit called the radian (rad) for angular measurements in circular motion.
Uniform circular motion: Movement in a circular path at a constant speed, but with continuously changing velocity due to direction change.
Frequency: Frequency is the reciprocal of the period: $f = \frac{1}{T}$ .
angular velocity: The rate of change of angular displacement. Its SI unit is radians per second (rad s⁻¹).
direction of centripetal: Always towards the center of the circular path.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 15 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

12.1 Kinematics of uniform circular motion.
The angular displacement of a body is the change in angle (radians, degree or revolutions) through which the body rotates around a circle.
Angular displacement is the ratio of: 𝛥𝜃 = 𝛥𝑠 𝑟.
A radian (rad) is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
Radians is usually written in term of π.
For a rotation for a complete circle (360 0 ), the radians is 2 π ( 𝛥𝜃 = 2πr/r).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q1(b)(ii)

PhysicsMay/June 2025

(b) (ii)

Calculate the period of rotation of the small cog.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/25

Question 2 of 29702/42 · Q1(c)(i)

PhysicsMay/June 2024

The metal disc in Fig. 1.1 has a radius of 9.3 cm. The centre of gravity of the modelling clay is 1.2cm from the rim of the disc and moves with a speed of 0.68 ms-1. (i) Calculate the angular speed ω of the disc.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

What are the key differences between linear and angular velocity?

Can an object in uniform circular motion have zero acceleration?

What provides the centripetal force in real-world examples?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q1(b)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS11.2 Fundamental particles NEXT →12.2 Centripetal acceleration

Discuss Kinematics of uniform circular motion

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Revise Kinematics of uniform circular motion for Cambridge 9702 (12.1)

Looking for free Physics 9702 notes on Kinematics of uniform circular motion? This A-Level lesson covers official syllabus point 12.1 on Paper 4: A Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Kinematics of uniform circular motion 9702 revision", "9702 12.1 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

12.1Physics25 min readPREMIUM

Kinematics of uniform circular motion

BY THE END, YOU CAN…

exam checklist — tick these off

1Define and use angular displacement, angular velocity, period, and frequency.
2Explain and calculate centripetal acceleration and centripetal force.
3Identify the source of centripetal force in various physical situations.
4Solve problems involving uniform circular motion using relevant formulas.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Kinematics of uniform circular motion

Cambridge 9702 Paper 4 — Kinematics of uniform circular motion (12.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
12.1 Kinematics of uniform circular motion.
2
The angular displacement of a body is the change in angle (radians, degree or revolutions) through which the body rotates around a circle.
3
Angular displacement is the ratio of: 𝛥𝜃 = 𝛥𝑠 𝑟.
4
A radian (rad) is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

What this topic covers

The official Cambridge syllabus points this lesson works through.

12.1.1
Define the radian and express angular displacement in radians
12.1.2
Understand and use the concept of angular speed
12.1.3
Recall and use $ω = 2\pi /T$ and $v = rω$

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure Live interactive1 / 4

Loading simulation…

Fetching from Physics Interactives by The Physics Classroom…

Rotational Motion

Both bugs share the angular speed, and linear speed is proportional to radius.

If the embed does not load, use Open simulation.

Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

Step-synced diagram — highlights what to look for in the simulation above.

Step 1

12.1 Kinematics of uniform circular motion.

16 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

16 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

PhETStart here · 1Java · best on a laptop9702 12.1–12.2 · IB A.4 · A.1
Ladybug Revolution
Spin a turntable with a ladybug on it and read angular position, velocity and acceleration alongside the linear values.
Why this one: Read angular position, angular velocity and linear speed side by side as the turntable spins.
Try this
1. Set a steady angular velocity — the ladybug’s speed stays constant.
2. Move the ladybug outward — same ω, larger linear speed.
3. Turn on the acceleration vector — it points to the centre.
Look for v = ωr and a = ω²r: further out means faster, with acceleration always toward the axis.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
PhysicsHubStart here · 29702 12.1 · 9702 12.2 · IB A.2
Circular Motion
Object in uniform circular motion; set radius, tangential speed, mass and size and watch the velocity (tangent) and centripetal acceleration (inward) vectors
Why this one: Velocity stays tangent while acceleration points to the centre: constant speed, changing velocity.
Try this
1. Double the tangential speed and watch the acceleration vector.
2. Double the radius instead.
3. Change the mass.
Look for Acceleration points to the centre with magnitude v²/r; the velocity vector stays tangent.
Open on PhysicsHub
PhysicsHub (@mattqdev) · MIT
SimuPhysicsStart here · 39702 12.1 · IB A.2
Angle and Arc Simulation
An angle at the centre of a circle is tied to the arc it cuts, showing that arc divided by radius is the angle in radians
Why this one: Arc length divided by radius is the angle in radians, whatever the radius.
Try this
1. Set an angle and read the arc length.
2. Double the radius and read the arc again.
3. Compare arc divided by radius with the angle.
Look for Arc length divided by radius equals the angle in radians.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsStart here · 49702 12.1 · 9702 12.2 · IB A.2
Drone in a Circular Tunnel
Fly a drone around a circular tunnel and inspect velocity and acceleration vectors
Why this one: Fly a circle and compare the velocity and acceleration arrows: always perpendicular.
Try this
1. Fly the drone around the circular tunnel and watch the velocity vector.
2. Compare the direction of the acceleration vector with the velocity vector.
Look for Velocity is tangential while acceleration points to the centre, perpendicular to it.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
The Physics ClassroomStart here · 59702 12.1 · 9702 12.2 · IB A.2
Uniform Circular Motion
Change the mass, speed or radius and see the velocity, acceleration and net force on an object moving in a circle
Why this one: Double the speed and the acceleration quadruples; double the radius and it halves.
Try this
1. Double the speed and read the acceleration.
2. Double the radius and compare.
3. Change the mass and compare the net force.
Look for Centripetal acceleration equals v² divided by r.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

More simulations11 more on this topic — core ones first

PhETCoreJava · best on a laptop9702 12.1–12.2 · 1.4 · IB A.1
Motion in 2D
Drag an object, or pick circular or elliptical motion, and watch the velocity and acceleration vectors.
Try this
1. Choose circular motion — velocity is tangential and acceleration points inward.
2. Choose elliptical — the acceleration no longer points at the centre.
3. Drag freely — speed up and watch the acceleration arrow swing forward.
Look for Uniform circular motion has constant speed but an acceleration toward the centre: v²/r.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
oPhysicsCore9702 12.1 · 9702 12.2 · IB A.2
The Conical Pendulum
Conical pendulum: adjust radius and view; see tension and weight resolving to give centripetal force
Try this
1. Increase the radius and watch the tension vector.
2. Change the view to look at the forces from the side.
3. Reduce the radius until the string hangs nearly vertical.
Look for The vertical component of tension balances the weight; the horizontal component supplies the centripetal force.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsCore9702 12.1 · 9702 12.2 · IB A.2
Circular Motion Simulation
The velocity and acceleration vectors are drawn as an object circles at steady speed
Try this
1. Watch the velocity vector round the circle.
2. Watch the acceleration vector.
3. Change the speed and compare the acceleration.
Look for Velocity is tangent to the circle and acceleration points towards the centre.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsCore9702 12.1 · 9702 12.2 · 9702 3.1
A Disk on a Turntable
Spin a turntable with a disk on it; find the speed at which friction can no longer hold it
Try this
1. Spin the turntable slowly and watch the disk stay put.
2. Raise the speed until the disk slides off; note the speed.
Look for Friction supplies the centripetal force until mv²/r exceeds the maximum friction, at which point the disk slips.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 12.1 · 9702 12.2 · IB A.2
Car on a Banked Road Problem 1
Drive a car on a banked curve; find the speed at which no friction is needed (banked up)
Try this
1. Drive the car around the banked curve and find the speed needing no friction.
2. Compare that speed with the banking angle.
Look for With no friction the horizontal component of the normal force alone supplies mv²/r, fixing one speed per banking angle.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 12.1 · 9702 12.2 · IB A.2
Car on a Banked Road Problem 2
Second banked-road case with the friction direction reversed
Try this
1. Drive the car around the curve and note the direction of friction.
2. Compare the speed with the no-friction case from Problem 1.
Look for Below the no-friction speed, friction acts up the slope to stop the car sliding down.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$1\text{ rad} = \frac{180^\circ}{\pi} \approx 57.3^\circ$

KEY RELATION

$f = \frac{1}{T}$

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KEY RELATION

$\omega = \frac{\Delta\theta}{\Delta t} = \frac{2\pi}{T} = 2\pi f$

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KEY RELATION

$v = \omega r$

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KEY RELATION

$a_c = \frac{v^2}{r} = \omega^2 r$

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KEY RELATION

$F_c = ma_c = \frac{mv^2}{r} = m\omega^2 r$

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Full topic notes

Formal explanation with the rigour you need for the exam.

What is Uniform Circular Motion?

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Angular Displacement ($\theta$) and the Radian

$1\text{ rad} = \frac{180^\circ}{\pi} \approx 57.3^\circ$

12.1 Kinematics of uniform circular motion.
The angular displacement of a body is the change in angle (radians, degree or revolutions) through which the body rotates around a circle.
Angular displacement is the ratio of: 𝛥𝜃 = 𝛥𝑠 𝑟.
A radian (rad) is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
Radians is usually written in term of π.
For a rotation for a complete circle (360 0 ), the radians is 2 π ( 𝛥𝜃 = 2πr/r).

Not clear?

Period ($T$) and Frequency ($f$)

$f = \frac{1}{T}$

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Angular Velocity ($\omega$)

$\omega = \frac{\Delta\theta}{\Delta t} = \frac{2\pi}{T} = 2\pi f$

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Linking Linear and Angular Speed

$v = \omega r$

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Acceleration in Circular Motion

Velocity is a vector quantity (magnitude and direction).
Constant speed means constant magnitude of velocity.
Changing direction means changing vector velocity.
A changing velocity means there is an acceleration.

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Centripetal Acceleration ($a_c$)

$a_c = \frac{v^2}{r} = \omega^2 r$

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Centripetal Force ($F_c$)

$F_c = ma_c = \frac{mv^2}{r} = m\omega^2 r$

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Sources of Centripetal Force

Gravitational Force: For a planet orbiting the Sun or a satellite orbiting the Earth, the force of gravity provides the centripetal force.
Tension Force: When you swing a ball on a string, the tension in the string provides the centripetal force.
Frictional Force: For a car turning on a flat road, the static friction between the tires and the road provides the centripetal force.
Normal Force: In a loop-the-loop roller coaster, a component of the normal force from the track on the car contributes to the centripetal force.
Electric Force: For an electron orbiting a nucleus in a simple atomic model, the electrostatic attraction provides the centripetal force.

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Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A satellite orbits Earth in a circular path with a radius of $7.0 \times 10^6$ m and a period of $90$ minutes. Calculate its linear speed and centripetal acceleration.

1
Convert period to seconds: $T = 90 \text{ min} \times 60 \text{ s/min} = 5400 \text{ s}$ .

EXAMPLE 2

1
First, list the known quantities: Mass, $m = 1200$ kg Linear speed, $v = 20$ m s⁻¹ Radius, $r = 50$ m

How it all connects

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MAIN IDEAKinematics of uniform circular motion

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Glossary

Key terms for this topic — skim now; the Check step will test them.

angular displacement: This is called angular displacement ( $\theta$ ). Instead of degrees, physicists often use a unit called the radian (rad) for angular measurements in circular motion.
Uniform circular motion: Movement in a circular path at a constant speed, but with continuously changing velocity due to direction change.
Frequency: Frequency is the reciprocal of the period: $f = \frac{1}{T}$ .
angular velocity: The rate of change of angular displacement. Its SI unit is radians per second (rad s⁻¹).
direction of centripetal: Always towards the center of the circular path.

10Apply

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0 of 6 answered

11Understand

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Your explanation — no notes

12Remember

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Your guess — write it before you look

1 / 15 · ← → space

Key takeaways

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close the tab only after these stick

12.1 Kinematics of uniform circular motion.
The angular displacement of a body is the change in angle (radians, degree or revolutions) through which the body rotates around a circle.
Angular displacement is the ratio of: 𝛥𝜃 = 𝛥𝑠 𝑟.
A radian (rad) is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
Radians is usually written in term of π.
For a rotation for a complete circle (360 0 ), the radians is 2 π ( 𝛥𝜃 = 2πr/r).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q1(b)(ii)

PhysicsMay/June 2025

(b) (ii)

Calculate the period of rotation of the small cog.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/25

Question 2 of 29702/42 · Q1(c)(i)

PhysicsMay/June 2024

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

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Frequently asked

What are the key differences between linear and angular velocity?

Can an object in uniform circular motion have zero acceleration?

What provides the centripetal force in real-world examples?

Checkpoint

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Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q1(b)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS11.2 Fundamental particles NEXT →12.2 Centripetal acceleration

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Revise Kinematics of uniform circular motion for Cambridge 9702 (12.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Ladybug Revolution

Circular Motion

Angle and Arc Simulation

Drone in a Circular Tunnel

Uniform Circular Motion

Motion in 2D

The Conical Pendulum

Circular Motion Simulation

A Disk on a Turntable

Car on a Banked Road Problem 1

Car on a Banked Road Problem 2

Key formulas

Full topic notes

What is Uniform Circular Motion?

Angular Displacement ($\theta$) and the Radian

Period ($T$) and Frequency ($f$)

Angular Velocity ($\omega$)

Linking Linear and Angular Speed

Acceleration in Circular Motion

Centripetal Acceleration ($a_c$)

Centripetal Force ($F_c$)

Sources of Centripetal Force

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Kinematics of uniform circular motion

Revise Kinematics of uniform circular motion for Cambridge 9702 (12.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Ladybug Revolution

Circular Motion

Angle and Arc Simulation

Drone in a Circular Tunnel

Uniform Circular Motion

Motion in 2D

The Conical Pendulum

Circular Motion Simulation

A Disk on a Turntable

Car on a Banked Road Problem 1

Car on a Banked Road Problem 2

Key formulas

Full topic notes

What is Uniform Circular Motion?

Angular Displacement ($\theta$) and the Radian

Period ($T$) and Frequency ($f$)

Angular Velocity ($\omega$)

Linking Linear and Angular Speed

Acceleration in Circular Motion

Centripetal Acceleration ($a_c$)

Centripetal Force ($F_c$)

Sources of Centripetal Force

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Kinematics of uniform circular motion