# Mathematics of Circular Motion

### Angular Displacement

The angle which an object moves around a circle is called the angular displacement. This angle is usually expressed in radians.

Hence, there are radians in one complete circle.

The relationship between the angle in radian and the circle is

where is the angular displacement in radians, and is the radius of the circle. The unit of is .

### Angular Velocity

Angular velocity is the rate of change of angular displacement.

Mathematically, angular velocity is

Since an object moves one circumference in one period time, we have

Eliminating ,

### Review

**Question 1**

An object moves round a circle of 15 cm radius at a constant speed. It completes one revolution in 8.0 s. Calculate its angular velocity and its velocity.

**Solution**