4.7 Radians & Angular Displacement

• 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:

• 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 (360^o) is equal to:

Radian Conversions

• If an angle of 360^o = 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

• The angular displacement Δθ is the ratio of:

• 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

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