Rolling pepper shaker on a slope
Although the rolling of a solid object is a mundane phenomenon in our daily life, its movement can be surprisingly complex and physically rich, particularly when the solid object has certain internal degrees of freedom, such as a half-filled plastic bottle of water. The translational and rotational motion of such an object couple in a highly nontrivial manner, often leading to seemingly unpredictable trajectories. We use a combination of experimental and theoretical approaches to analyze the rolling behaviors of a rigid cylinder that is partially filled with granular media, rolling on an inclined plane. We experimentally find a wide variety of rolling behaviors, including damped oscillation leading to a stop, meandering with avalanches coming to a stop, in addition to the stationary rolling and rolling with a constant acceleration. We address the occurrence of substantial slip during rolling, in contrast to what is often assumed. We classify the rolling behavior into three distinct phases and establish a phase diagram. We theoretically explain the transition between stopping and rolling and rationalize the phase boundary based on the rigid-body mechanics combined with the statics of granular media. Our study addresses the curiosity to understand the everyday phenomena and has significant implications for a wide range of physical applications from powder manufacturing technologies to robotics.