# Angular Speed Formula

Speed is all about how slow or fast an object moves. To calculate the speed of the rotational motion, angular speed arises.
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

$Angular\,&space;speed\,&space;\left&space;(&space;\omega&space;\right&space;)\,&space;=\,&space;\frac{Total\,&space;distance\,&space;traveled}{Total\,&space;time\,&space;taken}\,&space;=\,&space;\frac{\Theta&space;}{t}$

Distance traveled is in terms of angle θ is measured in radians and time taken in seconds. Therefore, the Angular speed is articulated in radians per seconds or rad/s.
Angular speed for a single complete rotation is known as

$\omega&space;\,&space;=\,&space;\frac{2\pi&space;}{t}$

The connection between Angular speed and Linear Speed is

$v\,&space;=\,&space;r\omega\,&space;=\frac{\Theta&space;}{t}$

Where,

Linear speed = v and
radius of circular path = r

Angular Speed Problems

Underneath are provided some questions on angular speed which helps you to get an idea of how to use this formula.

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

$angular\,&space;speed\,&space;is\,&space;given\,&space;by\,&space;\omega\,&space;=\frac{D}{T}$

$Where\,&space;D\,&space;=\,&space;Rotational\,&space;distance\,&space;traveled\,&space;=\,&space;2\pi&space;\,&space;and$

$T\,&space;=\,&space;365\,&space;\times\,&space;24\,&space;\times\,&space;60\,&space;\times\,&space;60$

$=31536000\,&space;S.$

$\therefore\,&space;Angular\,&space;Speed\,&space;\left&space;(&space;\omega&space;\right&space;)\,&space;=\frac{2\pi&space;}{31536000}$

$=\,&space;1.9923\,&space;\times\,&space;10^{-7}\,&space;rad/s.$

Question 2: The wheel of a wagon of radius 1m is traveling with the speed of 5m per second. Calculate its Angular speed.
Solution:

Given: Linear speed V = 5m/s,
Radius of Circular path r = 1m

$The\,&space;Angular&space;Speed\,&space;\omega&space;\,&space;=&space;\frac{V}{r}$

$=\,&space;\frac{5m/s}{1m}$

$=\,&space;5\,&space;rad/s.$