Car on a Banked Road
A car moving at velocity turns on a road banked at angle and radius of curvature . The horizontal component of the normal force acting on the center of gravity is equal to the centripetal force, which keeps the car on the road without skidding. The maximum velocity is .
The normal force has a vertical component that cancels the gravitational force: , where is the gravitational acceleration, and a horizontal component that causes the centripetal force: . Thus .