Banked Road

On a road banked at angle θ, the horizontal component of N provides centripetal force.

Ideal speed (no friction needed): v_ideal = √(rg tanθ).

With friction μ: v_max = √(rg(tanθ+μ)/(1−μ tanθ)); v_min = √(rg(tanθ−μ)/(1+μ tanθ)).

Banking reduces wear on tyres by not relying on friction alone.