OCR A Level Physics

Revision Notes

5.4.3 Angular Velocity

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Angular Velocity

Angular Displacement

  • In circular motion, it is more convenient to measure angular displacement in units of radians rather than units of degrees
  • Angular displacement is defined as:

The change in angle, in radians, of a body as it rotates around a circle

  • This can be summarised in equation form:

  • Where:
    • Δθ = angular displacement, or angle of rotation (radians)
    • S = length of the arc, or the distance travelled around the circle (m)
    • r = radius of the circle (m)

  • Note: both distances must be measured in the same units e.g. metres

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
  • It can be calculated using:

Angular Speed Equation 2

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

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

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

Angular Speed Equation 1

  • Where:
    • v = linear speed (m s-1)
    • r = radius of orbit (m)
    • T = the time period (s)
    • f = frequency (Hz)

 
  • Angular velocity is the same as angular speed, but it is a vector quantity
  • This equation shows that:
    • 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 ⍵)

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Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.