  This article illustrates the role of friction on the motion of a rolling
sphere on pedagogical example. We use a parabolic support rotating around it
axis to study the static equilibrium positions of a single sphere. Due to the
particular choice of the shape of support, some easy analytical calculations
allow theoretical predictions. (i) In the frictionless case, there is an eigen
frequency of rotation where the gravity balances the centrifugal force. All
positions on the parabola are therefore in static equilibrium. At others rates
of rotation, the sphere can go to the center or escape to infinity. It depends
only on the sign of the detuning with the eigenfrequency. (ii) In contrast, we
show that the static friction imposes a range of equilibrium positions at all
rotating rates. These predictions can be compared to the maximum equilibrium
radius measured on the experimental device. A reasonable estimate of the static
friction between the support and spheres made of different materials can be
extracted from this maximum equilibrium radius. To go further in understanding
of the experimental results, we perform a stability analysis also in the case
with friction. This analysis involves the rolling friction. We show that this
rolling friction can be estimated in the same device just by the check the
dissipation during the motion of the sphere.
