What are the physics of how a roller-coaster works?

Answer 1

A simple up-and-down roller-coaster relies on physics that are simple too. As a 1988 article in Science Times by William J. Broad explained, the train's potential energy, gained as a chain drive lifts cars through the earth's gravity to the top of that first drop, has been mostly converted to kinetic energy by the time the ride ends. The cars then coast to a stop (or close to it, often aided by brakes).

There are no engines, no motors, just gravity pushing riders along. Since speeding cars have no energy of their own, they can never climb higher than that first hill. Secondary hills get progressively smaller as the potential energy is used up.

The modern loop-the-loop roller-coasters that turn passengers upside down have a more complicated set of calculations built in. Many rely on the clothoid loop, a teardrop shape that makes it easy to turn people upside down without dropping them.

Designers previously had little success with a 360-degree circle. When entering such a circle, a speeding coaster car moves rapidly upward, generating a strong centrifugal force that presses riders into seats with too much energy. The danger at the top is just the opposite. The cars decelerate sharply, and if a car slows too much, gravity can pull riders from their seats while the cars are upside down.

By contrast, the clothoid shape smoothes out the acceleration so riders speed safely along the interior of the loop. The secret is the loop's changing radius, which controls the speed of the cars, varying it according to a scientific law known as the conservation of angular momentum. This principle can easily be visualized. The speed of a small weight tied to a string and whirled in a circle will be controlled by the radius of the circle. The weight will move slower if the string is lengthened, and faster if the string is shortened.

Elongating the circle into an elipse provides radii of varying lengths. Thus a comet in an elliptic orbit about the sun moves faster as it nears the sun, and slower when it is far away. So too, a coaster entering a teardrop loop moves relatively slowly as it arcs upward across a large radius at the bottom of the loop, lessening the centrifugal force on riders. At the top, the radius is much smaller. The coaster thus moves faster than it would in a circle, creating a greater centrifugal force to counteract gravity and keep riders safely in their seats..

Answer 2

Simple.
Kinetic and Potential energy.

Answer 3

just gravity