  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.
