Roller Coasters' Laws and Forces
Law #1: Newton's First Law of Motion states that an object at rest will tend to remain at rest while an object in motion will tend to remain in motion unless acted on by an unbalanced force. The unbalanced force on the object will change the speed of object, the direction of the object, or both. The resistance from the object to change its state of motion is known as inertia. An object's inertia is dependent on its mass. The two parts of Newton's first law: one, which predicts the behavior of stationary objects and the other, which predicts the behavior of moving objects.
Law #2: Newton's Second Law of Motion states that the unbalanced force exerted on the object is proportional to the object's mass and acceleration. The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Law #3: Newton's third Law of Motion states that for every action, there is an equal and opposite reaction. This means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.
Laws of Gravitation
Gravitational energy arises because of the gravitational force by which matter attracts other matter. Compared to other forces like electrical forces, gravitational forces are usually very weak. Gravitational energy is what makes roller coasters so thrilling. As the coaster is pulled up the first big hill, the gravitational energy is increased. When the coaster reaches the backside of the hill, the gravitational force is what causes it to accelerate. Much of the coaster's gravitational energy is converted to kinetic energy on the backside of the first hill. As the coaster climbs the second hill its kinetic energy is converted back into gravitational energy. Because the coaster's kinetic energy at the bottom of the first hill is less than its gravitational energy at the top of the first hill, the second hill is shorter than the first hill. If the second hill were the same height as the first one, the coaster would stop before the top of the second hill and start moving backwards. Every hill in the track must be shorter than the previous one, unless the coaster is again towed.
On a looping coaster, the general rules of centripetal force are in operation because the train is making a turn at every point during the loop. The force that makes the train turn through the loop is centripetal force. As the train starts the loop, gravity and momentum are pulling the train out of the loop, so the structure of the track provides the "seat force" that moves the train through the loop--the centripetal force. On it's upward climb, the train reaches a point where gravity is no longer pulling it out of the loop and thereafter it is acting as part of the centripetal force pulling the train toward the center of the circle. It is from this point until the top of the loop that it is important that the train has enough momentum to counteract the forces pulling it toward the center of the loop. That is a unique aspect of centripetal force on a vertical axis. There must be enough outward momentum to counteract the increase in centripetal force that occurs in the upper portion of the loop.
Centrifugal force is a perceived force, not an actual force. It can only be viewed from the vantage point of the spinning object. This is not a real force according to Newton's laws and is referred to as a pseudo-force. His concept is useful because it helps to explain the sensations a rider experiences while on a roller coaster.
For example, when analyzing the experience of a vertical loop, it is convenient to study the rider's sensations relative to the looping coaster rather than relative to the Earth. In order that Newton's laws are applicable in such a rotating frame of reference, an inertial force (the centrifugal force), equal and opposite to the centripetal force, must be included in the equations of motion. In a frame of reference attached to the looping coaster, the car is at rest. To obtain a balanced force system, the outward-acting centrifugal force must be included.