Angular Velocity Formula

Angular velocity formula

A physics concept that is applied to objects that move along a circular path is referred to angular velocity. 

Let us define the Angular velocity –

It is the vector measure of the rotation rate, which refers to how fast an object rotates or revolves relative to another point.

In short, the time rate at which an object rotates or revolves about an axis is called angular velocity. The Greek letter omega (ω, sometimes Ω) is used to denote angular velocity. It is measured in angle per unit time. 

Therefore, the SI unit of angular velocity is radians per second. 

Dimensional formula for angular velocity is [M⁰ L⁰ T^-1].

Every point on the object has the same angular velocity if we consider an object rotating about an axis. The points closer to the axis of rotation and those farther from the axis of rotation move at a different tangential velocity. The other names for angular velocity are rotational velocity and angular frequency vector.

Angular displacement is denoted by θ and t is given for change in time.

By convention, positive angular velocity indicates counter clockwise rotation, while negative is clockwise.  

Average angular velocity 

It is said to be the ratio of angular displacement to the time taken by the object to undergo the displacement and is denoted by ω_av.

                                  ω_av = angular displacement / time travel

Let us take some examples of the angular velocity formula

1. As per the minute hand of a clock calculate the angular velocity of it.

Solution:

In 60 minutes the minute hand completes one rotation

It displaces by 2π radians in

 60*60 seconds

 ω = 2π/360

     = 1.74 * 10^-3 rad/sec.

2. Find the angular velocity of a ball that is revolving in a circle of diameter 4 m with velocity 20 m/s

Solution:

radius of circle is given by diameter/2 

= 4/2

 = 2m

linear velocity is 20 m/s

angular velocity is v / r

ω = 20 / 2

 = 10 rad/sec