Why is centrifugal force considered fictitious, when it's the one that feels real to us when we are moving in a circle? I understand the explanation regarding the reference frames: if our body is the reference frame, and it is rotating, a fictitious centrifugal force needs to be made up to cancel the centripetal force and explain why we appear to be stationary in relation to ourselves. However, if we are in a round up ride, we feel pushed againsts the wall, rather than towards the center of the ride, which would be the centripetal force. So if centrifugal force is the fictitious one, wouldn't that be like saying that the force we feel pushing us againsts the wall is only in our minds?
The reason we feel that we are pushed outwards is due to inertia. Inertia is the resistance to movement. It is measured by mass. When we have more movement, it makes it harder to get us moving.
In a car that is on a curve, for example, our inertia makes us want to keep on going forward. Going forward in this case would make us feel that we are being pushed outwards. Therefore, there is no centrifugal force in this case.
Sometimes, the centrifugal force is referred to the reaction force of the centripetal force. But usually, it refers to a ficitious force used to simplify thr mathematics.
Suppose you're in a fast car and you stomp on the accelerator. You feel pressed into the back of the seat. In which direction are you accelerating? Forward, obviously, but you feel a force pushing against your back. Now you turn a corner. Your seatbelt, and maybe the door next to you, press against your side. In which direction are you accelerating? In this case, it's not so obvious, but it's inward, not outward. There is no centrifugal force here.
In both cases, the side on which you feel the force is opposite the direction in which you are accelerating.
We say fictitious because the actual source of the centrifugal acceleration is somewhat indirect and the experience one has results from the unbalanced forces acting on the reference frame, not a force. Note, it is an acceleration not a force.
For instance, imagine yourself on a swing. The swing seat is constrained to move in a circular arc by two opposing forces, gravity and tension. Those are the only two forces acting on the seat, yet while swinging, the seat is not in an inertial reference frame. So if you sit in the seat and constrain yourself to the seat (i.e., you don't fall off), you will be accelerated just like the seat because the tension and gravitational forces do not balance. The only place in the arc where you do not accelerate is same place where the seat would rest in equilibrium (i.e., just hanging there if left alone). Note that there is no centripetal or centrifugal force here, just tension and gravity. These two terms only apply to discussions of the acceleration of the reference frame or object. They are not forces and should not be called forces.
The point is that centrifugal acceleration only exists in non-inertial reference frames, namely frames of reference that are accelerating. It is not a force, only a term in the acceleration vector resulting from the frame of reference in which you calculate the acceleration. There is a useful animation found on the Coriolis effect Wikipedia page.