= Finite-friction qualification of a marginal rolling loop
At the limiting release height for a solid cylinder, the loop <normal force> is $N=(7mg/3)(1+\cos\theta)$ and the required static-friction magnitude is $mg|\sin\theta|/3$. Thus $|f|/N=|\sin\theta|/[7(1+\cos\theta)]$ diverges near the top, even though both <forces> vanish there. A finite <friction> coefficient therefore requires a height above the ideal contact threshold to maintain no-slip rolling throughout. A question imposing rolling but giving no coefficient determines the ideal limiting bound, not a realistic friction-dependent minimum.
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