## Circular motion

Table of Contents

Toggle### Uniform circular motion

The motion of a body moving with **constant speed along a circular path** is called **Uniform Circular Motion**.

An example of a uniform circular motion would be the hands of an analog clock. The tips of the clock hands move in a circular path at a constant speed.

#### Angular speed in sec^{-}^{1}

Angular velocity ω is **the time rate at which an object rotates or revolves about an axis**. It is measured in angle per unit time; hence, the SI unit of angular velocity is radians per second.

If a complete revolution (φ = 360° or 2 Π) is taken as a reference and as the associated time the rotation period T, the angular velocity can be calculated as follows:

#### Angular speed and rotational speed

The rotational speed is the number of revolutions per minute. If the speed is expressed in sec-1, the following applies:

#### Angular velocity and circular velocity

The circular velocity v corresponds to the velocity on a circular path and is proportional to the angular velocity ω and the radius r of the circular path.

**Example:** The belt speed of a conveyor belt is to be calculated. The nominal speed of the motor is 1410 rpm. A gearbox with a gear ratio of i = 15 is flanged to the motor shaft. The radius of the belt shaft is 5 cm.