The car of mass represented in the diagram on the left is moving at the velocity in a curve of radius . If the car is not skidding, the friction coefficient between the road and the tires is . As always, in order for the car to move in the curve, one of the forces acting on the car must be the one responsible for the centripetal force. On the car, two forces act on the vertical direction, the weight of the car and the reaction of the surface to this force or normal force . Clearly, these two forces cancel each other. However, there is a horizontal force directed to the center of the circle, this is the static frictional force between the road and the tires of the car . This force appears because the tendency of the car (tires) is to maintain the same state of motion (law of inertia) which corresponds to the car moving in a straight line.

Therefore, Newton's second law of motion applied to the car is with . On the other side of the equation, the acceleration is the centripetal acceleration, with the direction of the acceleration toward the center of the circle. Combining these relations, the following equation is obtained . In this equation, the necessary static frictional force increases as the square of the velocity. Remember that the magnitude of the static frictional force adjusts to the necessary value to prevent the object from skidding but only to a maximum limit. In the limit, where . Thus, the maximum value of the frictional force can be substituted in the previous relation to become from where . The last equation can be used to solve problems such as, for a given coefficient of static friction, what is the maximum velocity at which a curve may be taken, , etc.

by Luis F. Sez, Ph. D.    Comments and Suggestions: