Velocity is a vector quantity specifying both the speed and direction of movement of an object in a given frame of reference. The magnitude of velocity is the scalar quantity speed (S), related to distance (s) and time (t) by the equation S = s/t; similarly velocity (v) is related to distance and time by v = ds/dt. Angular or rotational velocity is given by ω = dθ/dt.
Angular velocity is the rate at which a rotating object sweeps out an angle relative to a fixed point. Angular velocity may be measured in radians, degrees, or revolutions per unit time.
The average angular velocity ω of an object moving from angle θ1 to θ2 in time t, is (θ1 - θ2)/t. Instantaneous angular veolcity is the value approached by ω as t tends to zero. The direction associated with the angular velocity of an object is perpendicular to the plane of its motion. The speed v of an object at a distance r from a fixed point is directly proportional to the magnitude ω of its angular velocity: v = rω.