For rotational motion about a point or axis, angular velocity is the rate of change of the angular position with time, or in other words the derivative of the angular position with time:
= angular velocity,  where  θ = the angular position 
t = time 

The direction of the angular velocity vector is perpendicular to the plane of rotation as given by the righthand rule. The angular velocity is expressed in units of [angular distance/time], often radians per second.
For an object moving in a curved path it can be useful to describe the motion using both angular and linear velocities. Using a fundamental relation for circular geometry:
where  θ = angle 


s = arc subtended by θ  

r = radius of the circle 
The magnitudes of the linear and angular velocities are related by:
where  v = linear velocity  
r = distance from the axis of rotation  

ω = angular velocity 
Note that we are not using vector notation in this expression, rather it is the magnitude of the velocities that follow the relation.
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