Angular velocity is a term that is commonly used in physics and engineering. It refers to the rate at which an object rotates around a fixed axis. Understanding the concept of angular velocity is important for a variety of applications, including robotics, aviation, and astrophysics.

## Definitions

Angular velocity is defined as the rate at which an object rotates around a fixed axis. It is measured in radians per second (rad/s) or degrees per second (deg/s). The formula for angular velocity is:

ω = Δθ / Δt.

Where ω is the angular velocity, Δθ is the change in angle over time, and Δt is the time interval.

## Origin

The concept of angular velocity has been around for thousands of years. It was first studied by the ancient Greeks, who used it to describe the motion of the stars and planets. The term “angular velocity” was first used in the 19th century by the French mathematician Augustin-Louis Cauchy.

## Meaning in different dictionaries

According to the Merriam-Webster dictionary, angular velocity is “the rate of change of angular displacement of a rotating body with respect to time.” The Oxford English Dictionary defines it as “the rate at which an object rotates around a fixed axis.”

## Associations

Angular velocity is closely related to other concepts in physics, such as angular acceleration, torque, and moment of inertia. It is also used in the design of machinery, such as engines and turbines, as well as in the control of robotic arms and other automated systems.

## Synonyms

Some synonyms for angular velocity include rotational velocity, spin rate, and angular speed.

## Antonyms

There are no direct antonyms for angular velocity, as it is a specific term used to describe a particular type of motion.

## The same root words

The root word for angular velocity is “angle,” which refers to the measure of the space between two intersecting lines or planes. Other related words include “rotation,” “spin,” and “revolve.”

## Example Sentences

- The angular velocity of the Earth around its axis is approximately 0.00007 radians per second.
- The robot arm was programmed to move at a constant angular velocity of 30 degrees per second.
- The centrifuge was spinning at a high angular velocity, causing the samples to separate quickly.
- The pilot adjusted the plane’s angular velocity to maintain a steady altitude.
- The moment of inertia of a rotating object is directly proportional to its angular velocity.