Now that I'm older, one of my favorite rides when the Punahou Carnival comes around is the Musik Express. However, when I was little, I found this ride very traumatizing. As far as I was concerned, this ride of little cars spinning rapidly in a circle on a tilt were going to make me die tragically. There was some force trying to throw me outwards, especially when I was on the outside edge, and unless I screamed very loudly the entire time my father was going to let me go to my death. At that time, I never understood why my father walked out of the ride like nothing happened and I fulfilled my adrenaline rush until the next carnival. But now I do :)
I was wrong when I thought that there was a force pulling me outward and away from the safety of my seat (Centrifugal force) but I was right that there were forces acting on me and keeping me on the ride (Centripetal force). The force of my weight, my father holding on to me, the friction caused by my seat, and the normal force from the side of the car all added together to create the forces that balanced out the force of the spinning ride. Because the angle of the cars change along different points of the ride, the value of each of these forces (except that of my weight) are constantly changing but could be calculated using the angle and radius from the car to the center.
Now that I understand that what I was feeling was a "fake force" or centrifugal force, I am much less afraid of the Musik Express and my safety riding it. Let's just hope that nothing ever goes so wrong that the Centripetal force never exceed its maximum magnitude - then I might fly out and have something to worry about.