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.

