Angular Velocity Formula

Introduction

Angular velocity is basically how fast an object rotates about an axis. From the rotation of wheels, orbit of planets, or maybe rotation of a fan blade, the angular velocity will help describe quantitatively the rate of rotation.

Angular velocity is most commonly expressed by the Greek letter ω. (ω) is the rate of variation of angular displacement with respect to time. In other words, the speed with which something rotates.

Formula For Angular Velocity 

The angular velocity formula is given by:

Where:

• ω = Angular velocity in radians per second, that is rad/s

• θ = Angular displacement in radians

• t = Time in seconds

Units

The standard unit of measurement for angular velocity is in terms of radians per second (rad/s). Note that when it comes to angular velocity, it is among those few physical parameters that has a magnitude and direction. The direction of angular velocity is along its axis of rotation.

Relationship Between Angular and Linear Velocity

The relationship between angular and linear velocity is one central feature of rotational dynamics. It helps in understanding the relation between the rotation of an object and the motion of points on its surface. 

Definition and Formula:

Angular velocity (ω) and linear velocity (v) are related to each other through the radius (r) of the circular path at which the object is rotating. The formula combining them is expressed as:

Where:

• v = Linear velocity in meters per second, m/s

• ω = Angular velocity in radians per second, rad/s

• r  = radius of the circular path in meters.

Solved Problem

Problem: Find the angular velocity of a particle moving along the straight line represented by at t = 5s.

Solution:

Given:

t = 5 s

 ω = 225 + 6

 ω = 231 units/sec