Final answer:
The riders in the barrel ride experience a normal force from the wall, which provides the centripetal force for circular motion, while gravity also acts on them. There is no actual centrifugal force in the inertial frame of reference.
Step-by-step explanation:
Understanding Forces in a Rotating Frame
When riders in an amusement park barrel ride feel as if they are being pinned to the wall, the sensation is due to the wall exerting a normal force on them. This force acts perpendicular to the wall's surface and provides the necessary centripetal force to keep the riders in circular motion.
In contrast to what riders might perceive, there is no centrifugal force acting on them in the inertial frame of reference; this is a fictitious force that only appears in the rotating frame. The only real forces acting on the riders are the gravitational force pulling them towards the Earth's center and the normal force from the wall, which provides the centripetal force necessary for their circular motion.