Converting potential energy into kinetic energy keeps your wild ride going after the first hill. You aren't riding in a machine with an engine. So physics is an important element of the attraction.
For more information about physics in rollercoasters, please go to: http://www.learner.org/interactives/parkphysics/coaster.html
Do you think you can make a great roller coaster while passing the safety tests? If so, design your own roller coaster at: http://www.learner.org/interactives/parkphysics/coaster/