(11)
is the pitch or advance per turn—a length which expresses the comparative motion of the translation and the rotation.
The pitch of a screw is the distance, measured parallel to its axis, between two successive turns of the same thread or helical projection.
Let r denote the perpendicular distance of a point in a body moving helically from the axis. Then
vr = αr
(12)
is the component of the velocity of that point in a plane perpendicular to the axis, and its total velocity is
v = √ {vx2 + vr2}.
(13)
The ratio of the two components of that velocity is