Very often we are interested in knowing how fast or how slow a body is rotating. It is determined by its angular velocity which is defined as "the rate at which the angular displacement is changing with time". Referring to figure given below, if ∆Ѳ is the angular displacement during the time interval ∆t, the average velocity ωav during this interval is given by,
The instantaneous angular velocity ω is the limit of the ratio ∆Ѳ/∆t as ∆t, following instant t, approaches to zero.
In limit when ∆t approaches zero, the angular displacement would be infinitesimally small, so it would be a vector quantity and the angular velocity as defined by the above equation would also be a vector. Its direction is along the axis of rotation and is given by right hand rule.
Angular velocity (ω) is measured in radians per second which is SI unit. Sometimes it is also given in terms of revolution per minute.
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