# Angular Velocity Formula

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

### Relationship Between Angular Velocity 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

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 Numericals

Solved Example

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

t = 5 s

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

ω = 9(52) + 6

ω = 225 + 6

ω = 231 units/sec

From the video you will learn that angular velocity is not just related to circular motion, instead, circular motion is a special case from which angular velocity is studied.