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 Fig. 5.1©, if ∆Ө is the angular displacement during the time interval ∆t, the average angular velocity ωav during this interval is given by

Fig 5.1 (c)

angular velocity equation 01

The instantaneous angular velocity ω is the limit of the ratio ∆Ө/∆t as ∆t, following instant t, approaches to zero.

angular velocity equation 02

In the 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 Eq. 5.3 would also be a vector. Its direction is along the axis of rotation and is given by right hand rule as described earlier.

Angular velocity is measured in radians per second which is its SI unit. Sometimes it is also given in terms of revolution per minute.

angular_velocity_image