## Revision Note

Author

Ann H

Expertise

Physics

• 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 =

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

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 =

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:

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

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

Table of common degrees to radians conversions

#### Worked example

Convert the following angular displacement into degrees:

#### Exam Tip

• 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!

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