• 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:

• 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:

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:

Radian Conversions

• 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