Final answer:
Riders in the spinning barrel of an amusement park ride feel pinned to the wall by centripetal force, which is the real force acting on them in an inertial frame of reference, along with gravitational force.
Step-by-step explanation:
In the described amusement park ride, riders are pinned to the wall due to the centripetal force. When the barrel spins, the riders are in motion with it, and the wall of the barrel provides the centripetal force needed to keep them moving in a circular path. The force that riders feel, sometimes mistaken for a centrifugal force, is actually the result of their body's inertia trying to move in a straight line while the barrel's wall forces them to move in a circle.
The gravitational force continues to act on the riders, pulling them down, but the normal force is removed when the floor drops away. Thus, the riders feel pinned to the wall by the centripetal force provided by the wall, and the two forces acting on them in this inertial reference frame are centripetal force and gravitational force.