Rolling without falling on an inclined treadmill

The motion of a cylindrically or spherically symmetric body on an accelerated treadmill, inclined of an angle $ heta $ with respect to the horizontal, is described by means of Newtonian mechanics. By assuming that the conveyor belt has an acceleration ${a_O}^{prime}$, not necessarily constant, and that the body rolls on it, we analyze the dynamics of the center of mass of the rolling body in the laboratory reference system. We find that, for given values of the acceleration (proportional to $gsin heta $), the center of mass does not move with respect to the laboratory reference system. This feature can be used at the 'engage' phase of the inquiry based science education approach in a lecture addressed to advanced high school students.