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# Physics of Bands and Curves

A bank in a racetrack is an upward slope toward the center of the track that is designed to hold objects such as cars and people on the track at high speeds and, thus, reduce the chance of the object going off the track. A curve is a bend in a track that has no upward slope, as in the case of a bank. Banks and curves within, for instance, the sport of auto racing are especially challenging because of the principles involved in classical physics.

English physicist and mathematician Sir Isaac Newton (1642–1727) stated within his first law of motion that any object of mass at rest will tend to stay at rest and any object in motion will tend to stay in motion at the same speed and direction unless acted upon by a force. The first law is often called the law of inertia because the term inertia means the resistance to motion. Because of inertia, the race car and driver, when coming upon a bank or a curve, would normally continue on a straight line on a racetrack if some force were not applied to them. Thus, the car and driver would miss the bank or curve and crash into the outside wall of the track or leave the track entirely.

In order for the race car to change direction—that is, to navigate through a bank or curve on a racetrack—a force must produce a change in direction (but not necessarily a change in speed) toward the center of the bank or curve. This type of force is called centripetal force (or center-seeking force), and it acts perpendicular to the car's velocity. It is defined as mv2/r, where, in this case, m is the mass of the race car traveling in a circular path of radius (r) at a constant velocity (v). (The equation changes if the racing track is not circular in shape; that is, if r is not constant.)

When the driver changes the direction that the tires are moving by rotating the steering wheel, friction is produced between the car's tires and the racetrack—that is, centripetal force is produced. As the equation implies, it is directly related to the square of the speed (the magnitude of the velocity) of the car. In the worst-case scenario, if the car is traveling too fast, the frictional force is not strong enough to hold the car on the racetrack. The centripetal force is also inversely related to the radius of the banking or curving track. The larger the radius of turning, then the less force needed to make it through the bank or curve.