For a banked circular road of radius r, banking angle θ and coefficient of friction μ, the maximum safe speed is given by:
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For a banked circular road of radius r, banking angle θ and coefficient of friction μ, the maximum safe speed is given by:

G1 Physics · Accepted Answer

At maximum speed, the vehicle tends to slip up the bank, so limiting friction f = μN_R acts down the slope. Resolving forces horizontally inward and vertically: N_R sinθ + f cosθ = mv²/r and N_R cosθ − f sinθ = mg. Substituting f = μN_R and dividing the two equations gives v_max²/(rg) = (sinθ + μcosθ)/(cosθ − μsinθ). Therefore v_max² = rg(sinθ + μcosθ)/(cosθ − μsinθ).