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If we have a car traveling in a circle on a banked curve without friction, the forces acting on the car would only be the normal force and gravitational force.

Using a x-y coordinate system, the horizontal component of normal (Nsintheta) provides the centripetal force Fc and it's vertical component (Ncostheta) cancels out the force of gravity. Everything works out here.

However, if you were to the draw the forces in a coordinate system that had axes parallel and perpendicular to the plane, you would find the normal force being canceled out by the force of gravity perpendicular to the plane (Fgcostheta) and leaving us with just a net force of the parallel force of gravity down the plane. What's stopping the car from sliding down the curve now and what's providing the centripetal force on this diagram?

Thank you.

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# Car on a Banked Curve (no friction)

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