# Angular Velocity and Angular Acceleration

Consider a rotating windmill. The velocity associated with windmills as they exhibit rotation about a fixed axis is angular velocity. In Physics, angular velocity is defined as the measure of the rotation rate. Or, in simpler words, it measures how fast an object rotates or revolves relative to another point. The time rate of change of angular velocity is known as the angular acceleration. Let us discuss the concepts of angular velocity and angular acceleration in detail in the following sections.

## What is Angular Velocity?

The time rate at which an object revolves or rotates is known as the angular velocity. It is represented by the Greek letter omega (ω, sometimes Ω). Angular velocity of an object is expressed as follows:

ω = Θ/ t

Where ω is the angular velocity, Θ is the angular displacement, and t is the change in time.

An object rotating in the counterclockwise rotation has positive angular velocity, and an object rotating clockwise has negative angular velocity.

### Angular Velocity – Examples

Some examples of angular velocity are:

#### Earth’s Angular Velocity

The angular velocity of the Earth can be calculated as follows:

ω = Θ/ t

ω = 2 π / 86400 seconds

Calculating the above, we get,

ω = 7.29 × 10-5 radians/second

The angular velocity of the Earth is  7.29 × 10-5 radians/second.

#### Hour-hand Angular Velocity

The angular velocity of the hour hand of a clock can be calculated as follows:

ω = Θ/ t

Substituting and calculating further, we get the angular velocity of the hour hand as follows:

ω = π / 21600 radians/second

## What is Angular Acceleration?

Angular acceleration is the time rate of change of angular velocity. Angular acceleration is measured in radians per second squared (rad/s2), and angular acceleration is usually denoted by the alpha (α).

## Frequently Asked Questions – FAQs

### Is angular velocity a vector or a scalar?

Angular velocity has both magnitude and direction; hence it is a vector quantity.

### Is angular velocity the same everywhere?

Angular velocity remains constant for every point on a rotating body.

### What are some examples of angular acceleration?

The motion of rotating objects such as the wheel, fan, and earth are studied with the help of angular acceleration.

### Can angular acceleration be negative?

Angular acceleration is considered negative if the angular speed increases clockwise.

### What is the relationship between angular velocity and angular acceleration?

An angular acceleration α is defined as the rate of change of angular velocity.

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