# Angular Speed Formula

Angular Speed Formula – Speed is simply the measurement of how fast or slow an object moves, for as how rapidly you drive your automobile. Now, we’re talking about a special form of speed. Angular speed is a sort of speed, however the body must follow a circular path. Angular speed is defined as the rate at which the central angle of a rotating body varies with respect to time. In this article, we will learn about angular speed.

## Angular Speed Formula

Angular speed is defined as the rate of change of angular displacement, or the angle travelled by a body in a circular route. Angular speed is calculated by comparing the number of rotations/revolutions performed by a body to the time taken. Angular speed is symbolised by the Greek letter ‘ω’, or Omega. The SI unit for angular speed is rad/s.

The angular speed is calculated using two different formula,

• ω = θ/t
• ω = v/r

## Angular Speed Formula Derivation

Despite the formula stated above, there is another and more widely used formula for calculation of angular speed from the point of view of competitive exams.

As ω = θ/t ⇢ (1)

Now we know that distance moved across arc of a circle is equal to radius times angle traversed. So,

s = rθ

=> θ = s/r ⇢ (2)

From (1) and (2),

Also from general understanding of linear speeds,

v = s/t ⇢ (4)

From (3) and (4),

ω = v/r

## How to Find Angular Speed

The rate at which the central angle of a spinning body alters with respect to time is measured as the angular speed. The link between angular speed and linear speed, as well as a few angular speed puzzles, is known as the Angular Speed Formula.

The earlier use of the word speed in many contexts. For instance, people should be aware of how quickly they are driving or pitching. Similarly to that, speed essentially refers to how quickly or slowly the object is going. So, the rate at which an item rotates is determined by its angular speed. In other words, it is defined as the change in the object’s angle per unit of time.

Therefore, one will need to know the angular speed of the rotating motion in order to compute its speed. The body’s travel distance is calculated using the Angular Speed Formula by multiplying the number of revolutions or rotations by the travel duration.

Additionally, the radian plays a significant role in this. People measure the angle in radians in order to determine the angular speed. According to this method of calculating angles, radians, the correct angle is defined as pi/2 radians. Therefore, 6.28 radians make up a complete rotation.

The rate at which an object changes its angles, which we measure in radians in a given time, is what we see as the angular speed. The magnitude of the angular speed is a single value.

Symbol ω = Θ/ t

Where:

The angular speed is represented by the symbol ω as radians/sec.

The angle in radians is represented by the symbol θ (2π  radians = 360 degrees).

t is the time, in seconds.

It is significant to notice that both angular velocity and angular speed employ the same Angular Speed Formula. The difference between the two is that whereas angular velocity is a vector quantity, angular speed is a scalar quantity.

A radian is a common unit for measuring rotational angle. The ratio of the two distances, radius and arc length, is what is known as a radius (a dimensionless unit).

A full rotation around a circular object’s circumference takes up 2π radians, or 360 degrees. Radian and degree can be converted using this relationship because they are interchangeable terms.

1 revolution = 2π radians = 360-degree

## Angular Velocity Solved Formula

Example 1: Consider a body travelling in a circular path of radius 8 m. It completes half a rotation in 8 seconds. Calculate the angular speed.
Solution:  In half revolution, the angle traversed is 180 degrees. In radians, it is equal to π radians.

ω = θ/t

=> ω = π/8 = 0.393 rad/s

Example 2: A car wheel of radius 4m is rotating with a linear speed of 40m/s. Calculate it’s angular speed.

Solution: ω = v/r

ω = 40/4