# Angular velocity

In circular motion, the magnitude that characterizes the speed with which the angle swept by the line connecting the rotating particle with the center of rotation is called angular velocity .

Summary

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• 1 Denotation
• 2 Another denomination
• 3 Example
• 4 Angular velocity as a vector
• 5 Source

Denotation

It is commonly denoted by the Greek letter omega ( ω ). In the International System of Units (SI) it is expressed in radians / second (rad / s). The modulus of the angular velocity of a body can be expressed as a function of the number of turns or revolutions the body performs in the unit of time, so it is sometimes given in revolutions per minute (rpm) or per second (rps).

Another denomination

The angular velocity is also known in physics as cyclic frequency .

For an object that rotates around an axis, each point on the object has the same angular velocity or for Uniform Circular Motion , the angular velocity is constant and is calculated using the formula:

ω = 2π / T, where T is the period of rotation.

Furthermore, as the period T = 1 / f, where f is the frequency of rotation, then the angular velocity can also be written by the relation:

ω = 2πf

Example

Representation of the three vector quantities ( angular velocity , radius vector and linear velocity )

When a mobile describes a circular path of center O, its position at any instant is given by the radius vector , r, and the angle, θ, formed by this vector and another fixed reference line in space. Its angular velocity, ω, is represented by an axial vector whose modulus is dθ / dt, its direction is perpendicular in O to the plane of rotation and whose direction is given, depending on the direction of rotation, by the right-hand rule .

When a solid rotates without sliding around a fixed axis, the points located on the axis are fixed, while the rest of the points are animated by circular movements whose centers are on the axis. Each of these points has a different linear velocity , v, but the angular velocity of all of them is common, ω, and is the angular velocity of rotation of the solid around the axis.

Angular velocity as a vector

The angular velocity is a vector that is perpendicular to the plane of rotation. To determine its direction as a vector, use the Right Hand Rule as shown in the image: