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First exams 2025

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Angular Speed (CIE A Level Physics)

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Leander

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Angular speed

  • The angular speed (⍵) of a body in circular motion is defined as:

The rate of change in angular displacement with respect to time

  • Angular speed is a scalar quantity, and is measured in rad s-1
  • Any object travelling in a uniform circular motion at the same speed travels with a constantly changing velocity
  • This is because it is constantly changing direction, and is therefore accelerating

Angular speed

Angular speed diagram, downloadable AS & A Level Physics revision notes

When an object is in uniform circular motion, velocity constantly changes direction, but the speed stays the same

Calculating angular speed

  • Taking the angular displacement of a complete cycle as 2π, the angular speed can be calculated using the equation:

omega space equals space fraction numerator increment theta over denominator increment t end fraction space equals space fraction numerator 2 straight pi over denominator T end fraction space equals space 2 straight pi f

  • Where:
    • Δθ = change in angular displacement (radians )
    • Δt = time interval (s)
    • T = the time period (s)
    • f = frequency (Hz)

  • Angular velocity is the same as angular speed, but it is a vector quantity
  • When an object travels at constant linear speed v in a circle of radius r, the angular velocity is equal to:

omega space equals space fraction numerator increment theta over denominator increment t end fraction space equals space v over r

  • Where:
    • v is the linear speed (m s-1)
    • r is the radius of orbit (m)

  • This equation tells us:
    • The greater the rotation angle θ in a given amount of time, the greater the angular velocity
    • An object rotating further from the centre of the circle (larger r) moves with a smaller angular velocity (smaller )

 

Worked example

A bird flies in a horizontal circle with an angular speed of 5.25 rad s-1 of radius 650 m.

Calculate:

a) The linear speed of the bird

b) The frequency of the bird flying in a complete circle

Answer:

Step 1: List the known quantities

  • Angular speed, ω = 5.25 rad s-1
  • Radius, r = 650 m

a)

Step 2: State the linear speed equation

v space equals space r omega

Step 3: Calculate linear speed

v space equals space 650 space cross times space 5.25 space equals space 3410 space straight m space straight s to the power of negative 1 end exponent space open parentheses 3 space straight s. straight f. close parentheses

b)

Step 2: Equate angular speed with the frequency equation

omega space equals space 2 straight pi f

Step 3: Rearrange to make frequency the subject

f space equals space fraction numerator omega over denominator 2 straight pi end fraction

Step 4: Substitute the known values to calculate

f space equals space fraction numerator 5.25 over denominator 2 straight pi end fraction space equals space 0.836 space Hz space open parentheses 3 space straight s. straight f. close parentheses

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Leander

Author: Leander

Expertise: Physics

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.