Angular velocity

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In physics, the angular velocity is a vector quantity (more precisely, a pseudovector) which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc. When measured in cycles or rotations per unit time (e.g. revolutions per minute), it is often called the rotational velocity and its magnitude the rotational speed. Angular velocity is usually represented by the symbol omega (Ω or ω). The direction of the angular velocity pseudovector is perpendicular to the plane of rotation, in a direction which is usually specified by the right-hand rule.[1]

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The angular velocity of a particle

Particle in two dimensions

The angular velocity of a particle in a 2-dimensional plane is the easiest to understand. As shown in the figure on the right (typically expressing the angular measures ɸ and θ in radians), if we draw a line from the origin (O) to the particle (P), then the velocity vector (v) of the particle will have a component along the radius (radial component, v) and a component perpendicular to the radius (cross-radial component, v_\perp). However, it must be remembered that the velocity vector can be also decomposed into tangential and normal components.

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