# Angular Speed Formula

## Angular Speed

The angular speed formula is used to calculate the distance the body covers in terms of rotations or revolutions to the time taken.

Speed is all about how slow or fast an object moves. Angular speed is the speed of the object in rotational motion.
Angular Speed Formula computes the distance covered by the body in terms of revolutions or rotations to the time taken. It is represented by ω and is given as

$$\begin{array}{l}Angular\,Speed=\frac{Total\,Distance\,Covered}{Total\,Time\,Taken}=\frac{\Theta }{t}\end{array}$$

Distance travelled is represented as θ and is measured in radians. The time taken is measured in terms of seconds. Therefore, the angular speed is articulated in radians per seconds or rad/s.

Angular speed for a single complete rotation is known as

$$\begin{array}{l}\omega =\frac{2\pi }{t}\end{array}$$

The connection between Angular speed and Linear Speed is

$$\begin{array}{l}v = R\omega\end{array}$$

Where,

Linear speed = v
The radius of the circular path = R

## Solved Examples

Problem 1: Earth takes 365 days to complete a revolution around the sun. Calculate its angular speed.

$$\begin{array}{l}Angular\,Speed=\frac{Total\,Distance\,Covered}{Total\,Time\,Taken}=\frac{\Theta }{t}\end{array}$$

where

$$\begin{array}{l}\Theta=\frac{2\pi}{31536000}\end{array}$$

t=365 * 24 * 60 * 60

=31536000 s

$$\begin{array}{l}\omega =\frac{2\pi }{31536000}\end{array}$$

Problem 2: The wheel of a wagon of radius 1m is travelling with the speed of 5m per second. Calculate its angular speed.
Solution:

Given: Linear speed V = 5m/s,
The radius of circular path r = 1m

$$\begin{array}{l}\omega =\frac{V}{r}\end{array}$$

Substituting the values, we get