First principles pivot-slide model of the motion of a curling rock: Qualitative and quantitative predictions

This paper is a sequel to a recent paper in which we proposed a quantitative “pivot-slide” model to explain the lateral motion (curl) of a curling rock. Here, we propose a physically-based, stick-slip mechanism to explain the brief rotation (pivoting) of the rock about a vertical axis passing through an ice pebble and the contact annulus of the rock. We view the motion of a rock as consisting of a sequence of pivots about individual ice pebbles, followed by “slides”, when the rock follows a straight-line path, while rotating about a vertical axis through its centre of mass. We have quantified this conceptual model and used it to make quantitative predictions of “total curl distance”, that are in general agreement with observations. The dynamical behaviour of the rock in the model is also consistent with many qualitative observations of curling rock behaviour, such as the direction of the lateral motion (curl) and the effect of sweeping in affecting the total curl distance. Our principal result is a simple, algebraic equation for the total curl distance of a curling rock. This expression contains many of the physical parameters involved in the game of curling.