Edexcel A Level Physics:复习笔记6.8 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:

• 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)