Curves are an essential part of a roller coaster, and centripetal acceleration is part of moving in a circular path. Therefore, centripetal acceleration is also an essential part of a roller coaster.
Centripetal acceleration points toward the center of the circular path of the train, but is felt by passengers as a force pushing them to the outer edge of the circular path. This feeling is often described as centrifugal force, although there is no actual force pushing or pulling passengers away from the circle. The “centrifugal force” is actually your body’s inertia, or its resistance to the train’s change in direction: your body wants to continue in a straight line and attempts to do so as the train turns. Luckily, your body is strapped into the roller coaster train, otherwise your body would continue in the straight path that the train was following before it entered the curve.
The equation for centripetal acceleration is:
ar = v2 / r
Where ar is centripetal acceleration, v is velocity in meters per second, and r is the radius of the circle in meters. This means that the higher the train’s velocity, the greater the centripetal acceleration. This also means that the smaller the curve of the path being traveled, the greater the centripetal acceleration. Because of this, many high-speed roller coasters use banked turns rather than the flat ones that are safe for slower speeds. Banking the turns in a roller coaster gives you the feeling of being pushed into your seat rather than being thrown to the side of the car.