Angular velocity is a vector quantity. In terms of magnitudes the speed of a point a distance r from the axis of rotation is given by v = r ω. The direction of the angular velocity, based on the sense of rotation of the rigid body, is given by a simple righthand rule.
A famous optical illusion. Most people initially see the girl spinning with angular velocity vector downward, but if you concentrate you can force your perception to reverse so that the girl's angular velocity vector is upward!


Unbanked curves! 
