What causes the feeling of "weightlessness" on pendulum rides?

Riders often experience near-weightlessness as they approach the top of a pendulum ride. If the ride is the type that makes a complete 360-degree circle, they experience a feeling of complete weightlessness. Read more here.

Feelings of weightlessness are not due to a decrease in forces of gravitation; people do not feel forces of gravity. What you feel is the force of a seat (or other external object) pushing on your body with a force to counteract gravity's downward pull. A 180-pound person at rest in his office chair experiences the seat pushing upwards on his body with a force of 180 pounds. Yet at the top of a pendulum ride, the same 180-pound person will feel less than this normal sensation of weight. At the very top of the pendulum ride, riders begin to fall out of their seats. Since a 180-pound person is no longer in full contact with his seat, the seat is no longer pushing on him with 180 pounds of force. Thus, the rider has a sensation of weighing less than his normal weight.

Why do riders experience high g-forces on pendulum rides?

As riders pass through the bottom of the circular arc, they often experience high g-forces. Once again, these g-forces are not evidence of increasing forces of gravitation, but the result of increases in the amount of force applied by the seat upon their bodies. Understanding this demands a little information about circular motion.

The motion of an object in a circle requires that there be a force directed toward the center of the circle (sometimes called a "centripetal force"). This means that at the bottom of the circular swing, there must be an upward force (since the circle's center is upward). Gravitational forces are always directed downward upon a rider's body; thus, gravitational forces cannot meet this centripetal force requirement. The seat must supply the centripetal force, pushing upwards on the rider with a force greater than gravity's downward pull. For a 180-pound person, the seat might have to supply 360 pounds of upward pull. This is twice the usual amount experienced by our 180-pound rider. For this reason, we would say the rider experiences 2 g's of force (a seat force that is 2 times the gravity force).

The most common pendulum rides include giant frisbee ride, pirate ship ride, and kamikaze ride.

Source: https://www.learner.org/exhibits/parkphysics/pendulum.html