  A magnetized bead in a magnetic field seeks to minimize its magnetic free
energy by aligning its magnetic moment with the field direction and by moving
towards the maximum of the field's intensity. However, when the bead is coupled
to a substrate it is forced to roll. The two otherwise independent degrees of
freedom, translation and rotation, become tightly coupled giving rise to subtle
and often counterintuitive effects. Here we investigate one such, easily
reproducible, yet stunning effect : A neodymium bead placed on top of a
laboratory magnetic stirrer. When the stirrer's magnet spins at slow rates the
bead naturally follows the field. However, surprisingly, at high spinning rates
the bead suddenly inverts its direction and runs, to the surprise of the
observer, in the opposite direction, against the driving field direction.This
effect, experimentally investigated in [J.Magn.Magn.Matter, 476, 376-381,
(2019)], is here comprehensively studied, with numerical simulations and a
theoretical approach complementing experimental observations.
