Radial Calculation:

$$-N_{x} = -m\frac{v^{2}}{R} $$ $$N\sin \theta = m\frac{v^{2}}{R} $$

Vertical Calculation:

$$N_{y} = mg$$ $$N\cos \theta = mg$$

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When a car moving on a parallel road enters a circular curve, the change in velocity direction results in a centripetal acceleration and the maximum velocity with which the car can travel on this road, without skidding, is determined by only the static friction of the road. But on a banked road the component of normal force and the static friction determines the maximum skidding velocity and is independent of the mass of the vehicle travelling on the curved circular road.