Roller coasters illustrate a few of the basic things of physics. Galileo knew most of the common physical principles that are similar to roller coasters now. A roller coaster train going down a hill represents an unsimple case of something going down in an inclined plane. Newton came up with the common physics needed to understand roller coasters, by showing a better understanding of forces. His first two laws in Newton's Laws in his "Principia" relate force and acceleration, which are main concepts in the physics of roller coasters. A force is a push or pull done to an object. Acceleration is a change in faster speed or direction. Newton was also one of the helpers in developing calculus, which is necessary to analyze falling things limited on more complex paths than inclined planes.
