A Cone Rotating in a Fluid Translates

Abstract

When a solid cone with smooth surfaces rotates at a constant rate about its long axis in still water, it will experience no friction, as announced earlier [ 1 ] and documented further here. However, if not restrained, it will translate along the axis base first and apex last, which is caused by a variation of pressure on its side: low near the base and high at the apex. This translation needs to be verified experimentally. Friction will occur during translation but an opposite reaction force will also take place related to the front to back asymmetry of the body [ 2 ]. Whether or not these two oppositely directed forces can cancel each other out by an appropriate choice of variable magnitudes is not known, but if true, it would lead to an extended translation. Also the translation path could be lengthened by slightly modifying the front face of the cone such that the translation itself produces rotation. One idea for such a modification is suggested. Observations in the future would be very beneficial.