Dynamics of a Rotating Sphere on Free Surface of Vibrated Granular Materials

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We investigate the rotational dynamics of a low-density sphere on the free surface of a vertically vibrated granular material (VGM). The dynamical behavior of the sphere is influenced by the external energy input from an electromagnetic shaker which is proportional to ε, where ε is equal to the ratio between the square of the dimensionless acceleration Γ and the square of the vibration frequency f of the container. Empirical results reveal that as the VGM transits from local-to-global convection, an increase in ε generally corresponds to an increase in the magnitudes of the rotational ω RS and translational v CM velocities of the sphere, an increase in the observed tilting angle θ bed of the VGM bed, and a decrease in the time t wall it takes the sphere to roll down the tilted VGM bed and hit the container wall. During unstable convection, an increase in ε results in a sharp decrease in the sphere's peak and mean ω RS, and a slight increase in t wall. For the range of ε values covered in this study, the sphere may execute persistent rotation, wobbling or jamming, depending on the vibration parameters and the resulting convective flow in the system.