Rolling Ribbons

Abstract

We present the results of a combined experimental and theoretical investigation of rolling elastic ribbons. Particular attention is given to characterizing the steady shapes that arise in static and dynamic rolling configurations. In both cases, above a critical value of the forcing (either gravitational or centrifugal), the ribbon assumes a two-lobed, peanut shape similar to that assumed by rolling droplets. Our theoretical model allows us to rationalize the observed shapes through consideration of the ribbon's bending and stretching in response to the applied forcing.