Theoretical and Experimental Studies on a Cylinder Containing Granules Rolling Down an Inclined Plane

TL;DR

This study combines theoretical modeling and experiments to analyze the dynamics of a granule-filled cylinder rolling down an inclined plane, revealing key insights into critical angles, oscillation frequencies, and energy dissipation.

Contribution

It introduces a theoretical framework for predicting the critical angle and oscillation behavior of a granule-filled cylinder, validated by experiments, independent of granule size distribution.

Findings

Critical angle is independent of granule size distribution.

Oscillation frequency varies with granular volume, peaking at an intermediate volume.

Energy dissipation depends on fractional volume and mass.

Abstract

The dynamics of a hollow cylinder containing granules and rolling down an inclined plane was investigated. A theoretical approach for investigating the behaviour of such a cylinder was proposed. The critical angle of the plane that allows the system to roll downward is presented. A simple experiment using six types of granules consistently confirmed the theoretical predictions. We showed that the critical angle is independent of the size distribution of the granules. We observed that the sliding angle of granules inside the cylinder is constant and, surprisingly, similar to the avalanche angle of the granules. Our theoretical prediction can be used to determine the critical angle without considering the shape, surface roughness and size distribution of the granules. Additionally, we derived the oscillation frequency of the system when it is slightly deviated from equilibrium, showing the frequency initially increases and then decreases with increasing granular volume. The oscillation is absent when the cylinder is empty or fully filled with granules. Furthermore, the dissipation of energy as a function of the fractional volume and fractional mass of the cylinder system were determined. This work might help students understand rolling motions other than the standard rolling motion commonly taught in the classroom.