In the absence of a force acting on an object, it continues to stay at rest or moves with a constant velocity. An object moving along a circular path, is not moving at a constant velocity. As velocity is a vector, the change is in the direction on motion of the object. To enable an object to move along a circular path, a force has to act on the object; this is known as centripetal force. The magnitude of centripetal force is given by `F = mr (4 pi^(2))/(T^(2))` where m is the mass of the object, r is the radius of the path it is moving in, and T is the time period of rotation.
For roller coasters, the radius, and time period have to be kept in mind to ensure there is sufficient centripetal force to enable the moving bodies to continue with their motion in the required path. If this is not done, the motion of the body along the desired path is not possible and this could lead to a serious accident. Centripetal force also has to be considered with respect to the force that people on the roller coaster can withstand. If the force in place is very high it could lead to people going unconscious or having a very bad feeling once the ride in the roller coaster is over.