Angular velocity

In physics, the angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, a pseudovector) which specifies the angular speed (rotational speed) of an object and the axis about which the object is rotating. This speed can be measured in the SI unit of angular velocity, radians per second, or in terms of degrees per second, degrees per hour, etc. Angular velocity is usually represented by the symbol omega (ω, rarely Ω).

The direction of the angular velocity vector is perpendicular to the plane of rotation, in a direction which is usually specified by the right-hand rule.

Angular velocity of a particle

Particle in two dimensions

The angular velocity of a particle is measured around or relative to a point, called the origin. As shown in the diagram (with angles ɸ and θ in radians), if a line is drawn from the origin (O) to the particle (P), then the velocity (v) of the particle has a component along the radius (radial component, v) and a component perpendicular to the radius (cross-radial component, v). If there is no radial component, then the particle moves in a circle. On the other hand, if there is no cross-radial component, then the particle moves along a straight line from the origin.

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