This article discusses a hexagonal prism rolling down an inclined plane, which is easy to realize experimentally and yields results that are consistent with a simple theory. This investigation would make an excellent undergraduate project.
In practice, a mixture of rolling and sliding can be observed for inclinations larger than the bound of .
It might be thought that it is possible to measure by a very simple experiment, namely to drop the pencil from a height onto a horizontal plane with the same material as the inclined plane. Then, measure the height to which the pencil rises after hitting the plane. The ratio of these heights gives the value of . However, there is no reason that such a method would give the same result as Eq. (9), because when the pencil hits the plane (in free fall), the force acting on it is distributed uniformly over the face of contact, whereas in the case of rolling, the force distribution is not uniform. Hence, the dissipation of energy is different and the value of would be different. This analysis is borne out by experiment, where I have found that the value of for the case of falling is between 0.1 and 0.3, while for rolling it is larger than 0.6.