Centripetal force is essential for a vehicle to navigate a curve, relying on friction between the tires and the road. According to Newton's third law, when a car turns, it exerts an outward force on the road, which is counterintuitive as it seems to oppose the centripetal force. This interaction is similar to a football player pushing off the ground to change direction, where the ground's reaction force propels the player. The discussion highlights that while the car and Earth exert equal and opposite forces, the Earth's mass results in negligible movement. Overall, the forces involved in cornering illustrate the complex dynamics of motion and friction in a vehicle's operation.