12.1.2 Angular Speed

• 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
• 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

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 cycle as 2π, the angular speed ⍵ can be calculated using the equation:

• 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:

• 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 ⍵)