Radians & Angular Displacement (Edexcel International A Level Physics)

Revision Note

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Chemistry

Radians

  • 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

  • Radians are used whenever describing the angular displacement of objects in circular motion 

  • Angular displacement can be calculated using the equation:

Radians Equation 2

  • 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 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 when using trigonometric functions - make sure this doesn’t happen to you!

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

Angular Displacement

  • The angular displacement Δθ is the ratio of:

Radians Equation 1

  • Angular displacement describes the change in angle, in radians, of a body as it moves in a circle
    • This angle is measured with respect to the centre of orbit

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

Exam Tip

Since the equation for angular displacement gives the angle in radians, make sure you're comfortable with then converting to degrees if you need to for the question!

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Richard

Author: Richard

Richard has taught Chemistry for over 15 years as well as working as a science tutor, examiner, content creator and author. He wasn’t the greatest at exams and only discovered how to revise in his final year at university. That knowledge made him want to help students learn how to revise, challenge them to think about what they actually know and hopefully succeed; so here he is, happily, at SME.

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