Rolling ribbons get the bends

For thousands of years, children have delighted in hoop rolling. Certainly, most of them have not considered that the rings are subject to gravitational and inertial forces; in any case, the hoops are stiff enough that they maintain their circular form despite those forces. But what happens to a rolling hoop that’s not so stiff? John Bush of the MIT mathematics department, along with visiting student Pascal Raux and colleagues, has answered that question in a recent study of more general systems—rolling bands that may be wider than they are high. Bush and company’s work was both experimental and theoretical. In their experimental investigations they took pictures of a vinyl polysiloxane loop placed on the inner surface of a rotating drum. The figure shows how the form of a representative loop changes as the drum speed is increased; blue corresponds to low speeds; red, high. In their theoretical work, the investigators confirmed the intuitive idea that the rolling band deforms as the inertial or gravitational force overwhelms the internal stiffness force. Indeed, if either gravity or inertial effects are strong enough, the top of the band can make contact with the bottom; new forces then come into play and the team’s analysis is no longer valid. Rolling droplets, tumbling blood cells, and carbon nanotubes deformed by van der Waals forces, the authors note, all display similar shapes to the rolling ribbons; the dynamics of those varied systems may be elucidated by the relatively simple ribbon study. (P. S. Raux ., Phys. Rev. Lett. 105 , 044301, 2010 http://dx.doi.org/10.1103/PhysRevLett.105.044301 .)