Angular Quantities

Consider a small particle moving in a circle with radius "r" along the circumference from point A to point B tracing an arc length "s"
. When the arc s = r ,  Ө = 1 radian measure, therefore Ө = s / r

Wher the angle Ө is measured in radians.

•  Ө is known as the angular distance.
•  s  is the linear distance (generally called  "d")

d  =  r  Ө

Since Ө = s / r (or Ө = d / r), we can relate the linear distance d to the angular distance  Ө using the simple equation:

Recall that This can be obtained by dividing the left side of the above equation by ∆t).

Dividing the right side of the same equation by ∆t we obtain the following .

The factor is known as the angular velocity.
The symbol for angular velocity is ω (pronounced "omega").  Its units are "radians per second -- rad/s".

Where and We can also express the angular velocity ω in terms of the frequency of rotation "f".

Starting from we get... Therefore:  ω = 2πf

In this case f is measured in revolutions per second (Hz) and ω is measured in radians per second

##### Similarly we can show that by dividing both sides of the equation by we can obtain expressions for acceleration. • The left side of the equation defines the linear acceleration "a".
• The right side of equation defines the angular acceleration "a(pronounced "alpha").

Recall that  in a full circle, the total radian/angular measure is  θ = 360

The linear distace around the circle, known as circumference, is d = 2 π r (the total circumference of the circle).