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.