title: Abrasion of flat rotating shapes.
abstract: We report on the erosion of flat linoleum "pebbles" under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with respect to the grid of pixels with a digital camera. This reduces digitization noise and allows the local curvature of the contour to be computed with a controllable degree of uncertainty. Several shape descriptors are then employed to follow the evolution of different initial shapes toward a circle, where abrasion halts. The results are in good quantitative agreement with a simple model, where we propose that points along the contour move radially inward in proportion to the product of the radius and the derivative of radius with respect to angle.
authors.affiliation: Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.
authors.forename: A E
authors.initials: AE
authors.lastname: Roth
authors.forename: C M
authors.initials: CM
authors.lastname: Marques
authors.forename: D J
authors.initials: DJ
authors.lastname: Durian