- Do not confuse with angular frequency
The unit for angular velocity is rad/s.
In physics, the angular velocity is a vector quantity (more precisely, a pseudovector) which specifies the angular speed, and axis about which an 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, 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 vector is perpendicular to the plane of rotation, in a direction which is usually specified by the right hand rule.
The angular velocity of a particle
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 φ 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 (tangential component, v⟂).
A radial motion produces no rotation of the particle (relative to the origin), so for purposes of finding the angular velocity the parallel (radial) component can be ignored. Therefore, the rotation is completely produced by the tangential motion (like that of a particle moving along a circumference), and the angular velocity is completely determined by the perpendicular (tangential) component.
It can be seen that the rate of change of the angular position of the particle is related to the tangential velocity by:
, the angle between vectors v∥
, or equivalently as the angle between vectors r
Combining the above two equations and defining the angular velocity as ω=dφ/dt yields: