Angular Velocity (Edexcel IAL Physics)

Spec point — 88

Angular Velocity

• The angular velocity ω* of a body in circular motion is defined as: The rate of change of angular displacement

• In other words, angular velocity is the angle swept out by an object in circular motion, per second

• Angular velocity is a vector quantity and is measured in rad s^–1

  • Since it is a vector, it has a magnitude (angular speed) and direction

• Angular velocity is calculated using:

ω = *$\frac{Δθ}{Δt}$

• Where:

  • Δθ = change in angular displacement (radians)
  • Δt = time interval (s)

• It is related to linear speed, v by the equation

v = ωr

• Where:

  • v = linear speed, v (m s^-1)
  • ω = angular speed (rad s^-1)
  • r = radius of orbit (m)

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

• Taking the angular displacement of a complete orbit or revolution as 2π radians, the angular velocity ω an be calculated using the equation:

• Where:

  • T = the time period (s)
  • f = frequency (Hz)

• This equation shows that:

  • The greater the rotation angle θ in a given amount of time T, the greater the angular velocity ω
  • An object travelling with the same linear velocity, but further from the centre of orbit (larger r) moves with a smaller angular velocity (smaller ω)

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 angular frequency of the bird

Answer:

Exam Hint Try not to be confused by similar sounding terms like "angular velocity" and "angular speed". Just like in regular linear motion, you have linear velocity and linear speed: one is a scalar (speed) and the other is a vector (velocity).

In this worked example, the equation v = rω is used to calculate the linear speed. This is fine, because v in this context is just the magnitude of the linear velocity (and similarly, ω is the magnitude of the angular velocity).

Finally, you may sometimes come across ω being labelled as 'angular frequency', because of its relationship to linear frequency f as given by the alternative equation ω = 2*πf. *Remember, the units of ω are rad s^–1, whereas the units of f are Hz.