AQA A Level Physics

Revision Notes

6.1.2 Radians

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:

Radians Equation 1

  • 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:

Radians Equation 2

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:
    • 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)

 

  • Radians are commonly written in terms of π
  • 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 conversions

Table 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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