OCR A Level Physics

Revision Notes

5.4.1 Radians

Test Yourself

Radians

  • In circular motion, it is more convenient to measure angular displacement in units of radians rather than units of degrees
  • The angular displacement (θ) of a body in circular motion is defined as:

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

  • The angular displacement is the ratio of:

θ = fraction numerator bold distance bold space bold travelled bold space bold around bold space bold the bold space bold circle over denominator bold radius bold space bold of bold space bold the bold space bold circle end fraction

  • Note: both distances must be measured in the same units e.g. metres
  • A radian (rad) is defined as:

The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle

  • Angular displacement can be calculated using the equation:

θ = bold S over bold r

Radians definition, downloadable AS & A Level Physics revision notes

When the angle is equal to one radian, the length of the arc (Δs) is equal to the radius (r) of the circle

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

 

  • Radians are commonly written in terms of π (Pi)
  • The angle in radians for a complete circle (360o) is equal to:

Radians Equation 3

Radian Conversions

  • If an angle of 360o = 2π radians, then 1 radian in degrees is equal to:

Radians Equation 4

  • Use the following equation to convert from degrees to radians:

Radians Equations 5

 

Table of common degrees to radians conversionsTable of common degrees to radians conversions, downloadable AS & A Level Physics revision notes

Worked example

Convert the following angular displacement into degrees:WE - Radians conversion question image, downloadable AS & A Level Physics revision notes

WE - Radians conversion answer image, downloadable AS & A Level Physics revision notes

Exam Tip

  • You will notice your calculator has a degree (Deg) and radians (Rad) mode
  • This is shown by the “D” or “R” highlighted at the top of the screen
  • Remember to make sure it’s in the right mode when using trigonometric functions (sin, cos, tan) depending on whether the answer is required in degrees or radians
  • It is extremely common for students to get the wrong answer (and lose marks) because their calculator is in the wrong mode - make sure this doesn’t happen to you!

Radians on calculator, downloadable AS & A Level Physics revision notes

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Ann H

Author: Ann H

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.