A special case of a particle trajectory on a circular cylinder occurs when there is no movement along the z axis: r ( t ) = r r ^ ^ + z z ^ ^ , where r and z 0 are constants. In this case, the velocity v P is given by: v P = d d t ( r r ^ ^ + z z ^ ^ ) = r ω ω θ θ ^ ^ = v θ θ ^ ^ , where ω ω is the angular velocity of the unit vector θ around the z axis of the cylinder.