title: Terminal retrograde turn of rolling rings.
abstract: We report an unexpected reverse spiral turn in the final stage of the motion of rolling rings. It is well known that spinning disks rotate in the same direction of their initial spin until they stop. While a spinning ring starts its motion with a kinematics similar to disks, i.e., moving along a cycloidal path prograde with the direction of its rigid body rotation, the mean trajectory of its center of mass later develops an inflection point so that the ring makes a spiral turn and revolves in a retrograde direction around a new center. Using high speed imaging and numerical simulations of models featuring a rolling rigid body, we show that the hollow geometry of a ring tunes the rotational air drag resistance so that the frictional force at the contact point with the ground changes its direction at the inflection point and puts the ring on a retrograde spiral trajectory. Our findings have potential applications in designing topologically new surface-effect flying objects capable of performing complex reorientation and translational maneuvers.
authors.affiliation: Department of Astronomy, University of California, Berkeley, California 94720, USA.
authors.forename: Mir Abbas
authors.initials: MA
authors.lastname: Jalali
authors.affiliation: Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, P.O. Box 11155-9567, Tehran, Iran.
authors.forename: Milad S
authors.initials: MS
authors.lastname: Sarebangholi
authors.affiliation: Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA.
authors.forename: Mohammad-Reza
authors.initials: MR
authors.lastname: Alam