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 in-tegral 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 parti-cles 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.
Newton's second lawvelocity integralform separation anglemathematica
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