5.2.1 Kinematics of circular motion

Okay so for those of you who take maths you can skip this paragraph as i'm just explaining about the radian. The SI unit for an angle is the radian. A radian is the angle subtended by a circular arc with length equal to the radius of a circle. One radian is approximately 57.3°. There are 2π radians in a complete circle. We can determine the angle in radians using the following equation:

angle in radians = arc length/radius

To describe the motion of moving objects we need to be able to describe their linear motion and also their circular motion. Any object moving in a circular path moves through an angle θ in a certain time (t). This gives a method of describing movement in terms of angular motion - the object will have an average angular velocity. The angular velocity (ω) of an object moving in a circular path is defined as the rate of change of angle:

ω = θ/t

If the object completes one full circle the time (t) will equal one period (T). This means that the object will move through an angle of 2π radians:

ω = 2π / T

NOTE: angular velocity is measured in radians per second. We can also express ω = 2πf as frequency is 1/T.

There are a few different units we can use express angular velocity (such as ° s^-1, rev s^-1, rmp, rad s^-1). We should use radians per second.