Reference frame and centrifugal force Imagine you are on a theme park ride in which you sit in a car and are spun around in a circle, basically like a giant centrifuge.
An observer from the outside would say that there is no centrifugal force acting on the person in the car, only centripetal. However, for the person in the car, there is the force pulling them inwards (centripetal), and its reaction force pushing outwards against the side of the car (centrifugal). However, from this point of observation, the person in the car is stationary and everything else is moving around him.
Does this not mean that there is no circular motion in this frame of reference, and therefore the reaction force is not centrifugal, as there is no circle centre?
Basically, I am confused as to why a fictitious centrifugal force will show up in a frame of reference where circular motion is not occurring.
 A: In the frame of the car it is not useful to talk about centripetal force.  In the rotating frame, you have two forces: the centrifugal force, and the real force of the of the side of the car pushing against you as the centrifugal force accelerates you toward the outside.  Note carefully that this force is not a reaction force to the centrifugal force.  
You say that the centrifugal force is the reaction force to centripetal force.  This is not true.  In the stationary frame you have centripetal force, but no centrifugal.  In the rotating frame you have centrifugal but no centripetal.  In neither frame do the two forces exist at the same time, so they can't be reciprocal. Further, centrifugal force has no "agent".  Forces occur as a result of an interaction between two systems.  One we call the "object" or "system" or "system in question", the other is the agent.  For gravity, I am the object, the earth is the agent.  Of course Newton 3 allows us to say that the earth is the object and I am the agent, and the forces in the two cases are equal and opposite.  Centrifugal force has no agent.  With that observation, it's clear that it is not a real force.  It does not arise from the interaction of two objects.  There is no reaction force to centrifugal force.
