Gravity-Driven Motion of a Particle on an Inclined Plane with Controlled Roughness

Abstract
We present an experimental and theoretical analysis of the motion of a single steel ball rolling on a rough inclined plane. This motion is well described by a Langevin equation with a viscous force. The constant of viscosity scales as (R/r)-3/2, where R is the radius of the rolling ball and r a length scale describing the roughness of the surface. We find, furthermore, that the average distance L* the ball rolls on the plane inclined at an angle θ is r exp [A(R/r)3 sin2 θ].
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