Air-drag and the Equilibrium of Whirling Threads

Abstract

IN the absence of all resistance to motion and assuming perfect flexibility, the differential equations of motion for a thread which carries a small spherical 'bob' and is whirled rapidly about a vertical axis by a horizontal arm give us an approximate solution for small amplitudes a plane sine wave—with reference to moving axes—leading to the well-known formula for plane vibrations¹. This approximate solution throws no light whatever on the stability of whirling threads as observed experimentally in air: these threads show 'necks' of appreciable amplitude in place of point nodes, the necks increasing in diameter the farther they are from the 'bob'. With sufficiently long threads and a large radius of the whirling arm, the sine outline disappears altogether.