# Angular Velocity Formula

## What is Angular Velocity?

Angular velocity is a vector quantity and is described as the rate of change of angular displacement which specifies the angular speed or rotational speed of an object and the axis about which the object is rotating. The amount of change of angular displacement of the particle at a given period of time is called angular velocity. The track of the angular velocity vector is vertical to the plane of rotation, in a direction which is usually indicated by the right-hand rule.

It is articulated as

$\omega\,&space;=\frac{d\Theta&space;}{dt}$

Where,

• dθ is change in angular displacement
• dt is change in time t

The formula for Angular Velocity is given by

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

• θ is an angular displacement
• t is the time taken

### Relationship Between Angular and Linear Velocity

The Angular Velocity and Linear Velocity is articulated by the formula

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

where,

• v is the linear velocity
• r is the radius of the circular path

Click on the link given below to know more about the relation between angular and linear velocity

Angular velocity is articulated in radian per second (rad/s). Angular Velocity formula is used to compute the angular velocity of any moving body.

## Angular Velocity Problems

Underneath, we have given some problems based on Angular velocity which may be helpful for you.

Solved Examples

Problem  1: Calculate the angular velocity of a particle moving along the straight line given by θ = 3t3 + 6t + 2 when t = 5s.
Given: θ = 3t3 + 6t + 2,
time t = 5 s

$The\,&space;angular\,&space;velocity\,&space;is\,&space;given\,&space;by\,&space;\omega\,&space;=\frac{d\Theta&space;}{dt}\,&space;=9t^{2}+6$

$For\,&space;t\,&space;=\,&space;5s,\,&space;the\,&space;angular\,&space;velocity\,&space;is\,&space;\omega\,&space;=\,&space;9(5)^{2}+6\,&space;=\,&space;181\,&space;units/sec.$

Problem 2: Find the angular velocity of the second hand of a clock?
$The\,&space;angular\,&space;velocity\,&space;is\,&space;given\,&space;by\,\,&space;\omega\,&space;\frac{\theta&space;}{t}$
$=\,&space;\frac{2\pi&space;}{60}$
$=\,&space;0.1047\,&space;rad/s.$