Variations in tension of an unwinding thread

The variations in tension occurring as a thread is pulled with uniform speed from a cylindrical spool are considered. For simplicity the steady state case when the thread follows a curve of constant shape on the surface of the spool is taken. It is shown that there is a limiting value, depending on the tension of winding and speed of the thread, for the angle with which the thread leaves the spool. Curves are given from which it is possible to estimate the variations in tension as the point of unwinding moves up the spool surface.