What is angle of friction prove that the tangent of angle of friction is equal to coefficient of static friction?
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Both are (top-down) engineering concepts. Both represent heuristic/phenomenological energy loss mechanisms used for mathematical convenience that are without fundamental descriptions. So a relationship between the two is not useful.
Using COF, μ and friction factors, fD lets you describe/predict a system's behavior conveniently and compactly, using mathematical equations and lookup tables. μ describes loss mechanisms in dry solids, and fD in fluids. They serve a mathematically similar purpose, and probably even share a lot of similar physics (both relate to thermal excitation and energy potentials of molecules at the bottom-end), but as engineering concepts, they are not related.
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