RESEARCH ON THE SLIDING PROBLEM OF PARTICLES ON ROUGH SURFACES

The motion of particles on a smooth hemisphere is a good research problem in high school. In this article, we extend this problem to any rough surface and derive the explicit integral form of velocity based on Newton's second law. It has an analytical expression in some cases and obtains a universal expression to determine the separation angle condition for particles leaving the surface, In the end, three curves, a circle, a parabola, and an ellipse, were analyzed in detail using Mathematica software, and several interesting conclusions were obtained.