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...