Simply speaking, a roller coaster is a machine that uses gravity and inertia to send a train of cars along a winding track. This combination of gravity and inertia, along with G-forces and centripetal acceleration give the body certain sensations as the coaster moves up, down, and around the track. The forces experienced by the rider are constantly changing, leading to feelings of joy in some riders and nausea in others. The basic principles of roller coaster mechanics have been known since 1865, and since then roller coasters have become a popular diversion.

When going around a roller coaster's vertical loop, the inertia that produces a thrilling acceleration force also keeps passengers in their seats. As the car approaches a loop, the direction of a passenger's inertial velocity points straight ahead at the same angle as the track leading up to the loop. As the car enters the loop, the track guides the car up, moving the passenger up as well. This change in direction creates a feeling of extra gravity as the passenger is pushed down into the seat.

At the top of the loop, the force of the car's acceleration pushes the passenger off the seat toward the center of the loop, while inertia pushes the passenger back into the seat. Gravity and acceleration forces push the passenger in opposite directions with nearly equal force, creating a sensation of weightlessness.

At the bottom of the loop, gravity and the change in direction of the passenger's inertia from a downward vertical direction to one that is horizontal push the passenger into the seat, causing the passenger to once again feel very heavy. Most roller coasters require passengers to wear a safety harness, but the forces exerted by most loop-the-loop coasters would keep passengers from falling out.

G-forces (gravitational forces) create the so-called "butterfly" sensation felt as a car goes down a hill. An acceleration of 1 standard gravity (9.8 m/s2) is the usual force of Earth’s gravitational pull exerted on a person while standing still. The measurement of a person's normal weight incorporates this gravitational acceleration. When a person feels weightless at the top of a loop or while going down a hill, they are in free fall. However, if the top of a hill is curved more narrowly than a parabola, riders will experience negative Gs and be lifted out of their seats, experiencing the so-called "butterfly" sensation.

See also:
https://en.wikipedia.org/wiki/Physics_of_roller_coasters
https://en.wikipedia.org/wiki/Roller_coaster
https://en.wikipedia.org/wiki/Roller_coaster_elements

Source: Wikipedia (All text is available under the terms of the GNU Free Documentation License and Creative Commons Attribution-ShareAlike License.)