No abstract

The initial acceleration of a rigid rod rotating around one end, and the time required for the rod to fall onto a horizontal table, is compared with the acceleration and falling time of a free particle originally placed on the rod. The conditions under which the rod falls faster than the particle are established. Three cases are identified. The third case, in which the particle catches up with the rod, has not, to the author’s knowledge, been published previously.

This article discusses the rolling motion on a rough plane of a wheel whose center of mass does not coincide with the axis; for example, when a heavy particle is fixed to the rim of a rigid hoop. In cases with large eccentricity, the resulting motion is surprisingly complex, with four phases being identified, namely rolling (without slipping), spinning, skidding, and “hopping,” by which is meant that the wheel actually leaves the plane. The main result of this analysis is the identification of the conditions that are required for hopping to occur. A second result is that faster than gravity accelerations occur when the mass of the particle is greater than the mass of the hoop. Massless hoops are briefly discussed as a special case of the general results.

We report the results of an experiment on the rolling motion of a loaded hoop. The data are obtained using a high-speed video camera, and the motion is analyzed on a frame-by-frame basis. Our analysis demonstrates that the experimental results are in reasonably close agreement with previously reported theoretical results.

For many years it was believed that a rigid, massless hoop which is loaded with a heavy particle on its rim and rolling on a rough surface would hop when the normal reaction became zero. This is a hypothetical model that raises a number of very interesting and subtle aspects of dynamics. In this paper the motion of such hoops is analyzed in detail, and a new motion with unusual characteristics is found.