• 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:

• 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)