Investigation Of The Motion Of A Fixed RotatingSolid Body Over Ice With A Thin Fluid Interface

Abstract

This article contains a theoretical investigation of the frictional forces on a solid body, such as a curling stone, rotating about a fixed axis, where the retarding force is due to the viscous drag of a thin water layer overlying a thick ice layer. Most introductory physics texts state that this deceleration is due to frictional surface forces, with a constant coefficient of sliding friction. Here, we proceed under the assumption that a fluid boundary layer is formed between the surface of the solid body and the ice as a result of pressure melting. In addition, the interface between the water and ice phases is considered to be a Stefan problem. The resulting fluid layer is responsible for the viscous drag forces that slow and eventually stop the rotating solid body. As a special case, a similar problem obtained by neglecting curvature is examined where the problem may be expressed in Cartesian coordinates rather than radial coordinates. Thus instead of a rotating curling rock, the physical problem is represented by a finite skate blade moving in a straight line over an ice surface with a fluidized interface. To calculate the drag forces experienced by the skate blade we first determine the temperature distribution of the water/ice interface, which requires the solution of a two-dimensional free boundary problem. A simplified problem is considered where the depth of the boundary layer is assumed to be independent of the horizontal position, and thereby we find expressions for the temperature of the water and ice in addition to an expression for the position of the ice water interface. Upon obtaining these results we can calculate the approximate drag experienced by a finite skate blade. At this point we can perform a similar analysis in radial coordinates providing a first approximation of the viscous drag forces of a rotating curling stone.