What is uniform circular motion in the context of Cambridge International A Levels Physics?

Uniform circular motion refers to the motion of an object traveling at a constant speed along a circular path. In Cambridge International A Levels Physics, this concept is crucial as it involves understanding how velocity, acceleration, and force interact in circular motion, despite the speed being constant.

How is centripetal acceleration calculated in uniform circular motion?

In uniform circular motion, centripetal acceleration is directed towards the center of the circle and is calculated using the formula a_c = v^2/r, where v is the linear speed of the object and r is the radius of the circular path. This acceleration is responsible for changing the direction of the velocity vector, keeping the object in circular motion.

Why is velocity considered a vector quantity in uniform circular motion?

Velocity is considered a vector quantity because it has both magnitude and direction. In uniform circular motion, even though the speed (magnitude of velocity) remains constant, the direction of the velocity vector continuously changes as the object moves along the circular path. This change in direction is what necessitates the presence of centripetal acceleration.

What role does centripetal force play in uniform circular motion?

Centripetal force is the net force required to keep an object moving in a circular path at constant speed. It acts towards the center of the circle and is essential for maintaining the circular motion. The magnitude of this force can be calculated using F_c = m*v^2/r, where m is the mass of the object, v is its speed, and r is the radius of the circle.

Can you explain the difference between angular velocity and linear velocity in uniform circular motion?

In uniform circular motion, angular velocity (ω) refers to the rate at which the object rotates around the circle, measured in radians per second. Linear velocity (v), on the other hand, is the rate at which the object moves along the circular path, measured in meters per second. The two are related by the equation v = ω*r, where r is the radius of the circle. Understanding both concepts is crucial for solving problems related to motion in a circle in Cambridge International A Levels Physics.

Why is "Using degrees instead of radians" a common mistake in Kinematics of uniform circular motion?

Why it happens: Habit. How to avoid it: Angular velocity is always in RADIANS per second in physics formulas. Convert if needed. Source: 9702 Examiner Reports 2022-2024

Motion in a CircleCambridge International A Levels Physics (9702)

Kinematics of uniform circular motion

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Kinematics of Uniform Circular Motion Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Angular vs linear quantities. Period and frequency. Radians.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

12.1.1 — Define angular velocity.
12.1.2 — Relate linear and angular.
12.1.3 — Use period and frequency.

Angular vs linear

$v = r\omega$ .

Angular velocity $\omega$ = rate of change of angular position. Units: rad/s.

Linear (tangential) speed at radius $r$ : $v = r\omega$ .

Period $T$ = time for one full revolution. $T = 2\pi/\omega = 1/f$ .

Frequency $f$ = revolutions per second. Units: Hz = rev/s.

Common conversions.

1 rev = $2\pi$ rad = $360°$ .
$\omega = 2\pi f$ .
$f = 1/T$ .

Cambridge tip. Always work in radians for physics formulas.

$\omega = 2\pi/T$ .
$v = r\omega$ .
Use radians.

See the full worked example for kinematics of uniform circular motion →

How it’s examined

Circular kinematics on every Paper 4. Most-tested: $\omega$ conversion (4-5 marks), $v = r\omega$ (5 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — Kinematics of uniform circular motion

Step-by-step solutions to past-paper-style questions on kinematics of uniform circular motion, written exactly the way a tutor would explain them at the board.

1Angular velocity (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• angular velocity
Question
A wheel rotates at 5.0 revolutions per second. Find angular velocity $\omega$ in rad/s. (5 marks)
Step-by-step solution
1. Step 1
  1 revolution = $2\pi$ rad.
  $\omega = 5.0 \times 2\pi \approx 31.4 \text{ rad/s}$
Answer
$\omega \approx 31.4$ rad/s.
2Linear speed (5 marks)
Extended• linear speed
Question
A point 0.30 m from the axis of rotation has angular velocity 12 rad/s. Find its linear speed. (5 marks)
Step-by-step solution
1. Step 1
  $v = r\omega$ .
  $v = 0.30 \times 12 = 3.6 \text{ m/s}$
Answer
$v = 3.6$ m/s.
3Period from frequency (4 marks)
Extended• period
Question
An object completes uniform circular motion at 50 Hz. Find its period and angular velocity. (4 marks)
Step-by-step solution
1. Step 1
  $T = 1/f$ .
  $T = 1/50 = 0.020 \text{ s}$
2. Step 2
  $\omega = 2\pi/T = 2\pi f$ .
  $\omega = 100\pi \approx 314 \text{ rad/s}$
Answer
$T = 0.020$ s; $\omega \approx 314$ rad/s.

Key Formulae — Kinematics of uniform circular motion

The formulae you need to memorise for kinematics of uniform circular motion on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Angular velocity
$\omega = \dfrac{2\pi}{T} = 2\pi f$
$\omega$
angular velocity (rad/s)
$T$
period
$f$
frequency
When to use
Rate of change of angular position.
Linear from angular
$v = r\omega$
$r$
distance from axis
When to use
Linear speed at radius $r$ on rotating body.

Key Definitions and Keywords — Kinematics of uniform circular motion

Definitions to memorise and the exact keywords mark schemes credit for kinematics of uniform circular motion answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Angular velocity
Examiner keyword
Rate of change of angular position. $\omega = d\theta/dt$ . Units: rad/s.
Uniform circular motion
Examiner keyword
Motion in a circle at constant SPEED (but changing direction, so accelerating).

Common Mistakes and Misconceptions — Kinematics of uniform circular motion

The traps other students keep falling into on kinematics of uniform circular motion questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Using degrees instead of radians
9702 Examiner Reports 2022-2024
Why it happens
Habit.
How to avoid it
Angular velocity is always in RADIANS per second in physics formulas. Convert if needed.

Practice questions

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Past paper style quiz

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Kinematics of uniform circular motion — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Kinematics of uniform circular motion

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Angular velocity (5 marks)

2Linear speed (5 marks)

3Period from frequency (4 marks)

Angular velocity

Linear from angular

Angular velocity

Uniform circular motion

✕Using degrees instead of radians

Practice questions

Past paper style quiz

Assess your understanding

Kinematics of uniform circular motion — frequently asked questions