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.

1.
Problem 6 of 1995 Boston Area Undergraduate Physics Competition, ⟨liquids.seas.harvard.edu/oleg/competition⟩.
2.
Problem 1 of the 29th International Physics Olympiad (
1998
3.
T.
McGeer
and
L. H.
Palmer
, “
Wobbling, toppling, and forces of contact
,”
Am. J. Phys.
57
,
1089
1097
(
1989
).
T.
McGeer
, “
Passive dynamic walking
,”
Int. J. Robot. Res.
9
,
62
82
(
1990
).
4.

In practice, a mixture of rolling and sliding can be observed for inclinations larger than the bound of $μ>tanθ$.

5.

It might be thought that it is possible to measure $ϵ$ by a very simple experiment, namely to drop the pencil from a height $h0$ 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 $ϵ$. 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 $ϵ$ would be different. This analysis is borne out by experiment, where I have found that the value of $ϵ$ for the case of falling is between 0.1 and 0.3, while for rolling it is larger than 0.6.

6.
See EPAPS Document No. E-AJPIAS-77-023905 for the program and sound files. For more information on EPAPS see http://www.aip.org/pubservs/epaps.html.
7.
A.
Domenech
,
T.
Domenech
, and
J.
Cebrian
, “
Introduction to the study of rolling friction
,”
Am. J. Phys.
55
,
231
235
(
1987
);
D.
Shaw
, “
Frictional force on rolling objects
,”
Am. J. Phys.
47
,
887
887
(
1979
).