In a recent paper,1 De Luca works out how a thin disk can be rested on a rough incline by adhering an additional mass at its rim. De Luca’s analysis is correct and rigorous, but I think it may be difficult for most high school students, and the physics of the solution(s) need to be more elaborated. Here is an alternative, and comparatively simpler approach.

Denote the center, radius, and mass of the disk as C, R, and M, respectively, the additional mass as m, and the sloping angle of the incline as θ. The center of mass (CM) of the composite disk-and-m object is at a distance r from C on the line connecting C and m, where r = mR/(M + m).2 Hence,


where ρ = M/m....

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