# Why is centrifugal force considered fictitious, when it's the one that feels real to us when we are moving in a circle?

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?

• You may not have given enough thought to what "we feel pushed" means. If you think through some more day-to-day instances you'll find that there are two different ways to interpret that phrase. One that is consistent with the way we talk about gravity and one consistent with the way we talk about everything else. There is a reason for this. How does it feel if a friend pushes you unexpectedly from behind; how does your body move and how do your loose limbs move. What happens if a sliding sidewalk stops unexpectedly (noting that it is only in contact with your feet). Commented Oct 19, 2015 at 20:14
• Obligatory xkcd.com/123
– rob
Commented Oct 20, 2015 at 5:13

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.

• So which force makes us feel pushed againsts the wall in a round up ride? From your answer I understand it is not the centrifugal force. Is that a third law partner to the centripetal force? I'm a little confused about how to name the force acting on our body outward from the the center of rotation, which feels like a real force. Commented Oct 19, 2015 at 21:02
• @Auggie -- There is no outward force acting on you. The forces acting on you are gravitation, which pulls you downward, friction against the wall, which opposes gravity, and the normal force by the wall, which pushes you toward the center of the ride. Commented Oct 19, 2015 at 21:07
• So, just to clarify, when you say there is no outward force acting on us, you mean in an inertial reference frame, right? what about in a rotating reference frame? And then, going back to my original question, is the force that we feel in the outward direction only an illusion? I'm a beginner and an amature, so I appreciate your patience :) Commented Oct 19, 2015 at 21:20
• @Auggie - What you feel in that ride is very similar to what you feel in an accelerating car when the back seat of the car pushes on you. I hope you agree that there's no force pushing you into the seat. It's the same for the ride. That push by the wall of the ride (or by the back of the car seat) against you propagates through your body. Your body is a mix of bones, cartilage, and soft tissues that respond differently to that push. You feel that push internally as well as externally. Commented Oct 19, 2015 at 21:23

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.

• The idea of centrifugal force is not used to simplify the mathematics. Just the opposite. Centrifugal force exists only in the rotating frame of reference, and it complicates things. Much simpler to analyze the situation from a non-rotating frame of reference, where it becomes obvious that a body can not revolve around the center unless a real force continually pushes it toward the center. Commented Oct 19, 2015 at 22:28
• Why the downvote? How can I improve my answer? Commented Oct 20, 2015 at 18:01

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.

Centrifugal force is actually fictitious.

What someone feels while turning in a car along a circular path is their inertia, but their brain perceives it as if a force is acting outwards.

There is no force acting outwards; it is just your inertia trying to keep you moving in a straight line. As the car turns, you feel as if you are being thrown off because you are trying to go in a straight line, but the car has already rotated, and your brain perceives that you are thrown outwards.

This can be seen when a person falls out of a car trying to turn—they fall tangentially, not centrifugally. Whenever someone falls off a merry-go-round, they move tangentially, not outwards opposite to the centripetal force.

Let me make it more clear. When you are in a car that is accelerating, you perceive yourself to be at rest and the surroundings to be moving in the opposite direction of your acceleration with the same magnitude. So, you add a fictitious pseudo force acting along the direction of the acceleration of the surroundings as perceived by you because, without force, there cannot be acceleration.

But is there any force acting on the surroundings? Hell no.

The same applies to a stone being rotated: an observer on it adds a pseudo force known as centrifugal force, which balances the inward force so that, in the stone's frame of reference, it appears to be at rest, as shown using a free-body diagram (FBD) and forces.

The observer confuses the pseudo force known as the centrifugal force that they added with the inertia trying to throw them off tangentially.

Is the rest thing true for the observer in the car too? Of course, yes. Because the person in the car perceives himself to be at rest, he also has to add a pseudo force opposite to the force of the engine that accelerates the car so that the net forces on him and the car are zero.

There are many people who already answered the question. I just want to point out that you told "a fictitious centrifugal force needs to be made up to cancel the centripetal force" but it never happens. Centripetal force never cancels out centrifugal force.

Actually, it matters from which frame you are observing. As an example, suppose you are seeing earth is revolving around sun, now write down the equation of motion of earth. You know to revolve around the sun the earth needs some centripetal force to be in the motion and who is providing this Gravitational Force between earth and sun.

so, $$\frac{mv^2}{R}(-\hat{r})=G\frac{mM}{R^2}(-\hat{r})$$ [here exists the centripetal force]

Now, you are seeing the same situation from a different frame where you are on the sun and revolving with the same angular velocity of earth's revolution around sun. You will see the earth is static. But the gravitational force still there which is attracting earth towards the sun, there is no force against the attraction as observed by you, but you still see the earth is static.

Which means, $$-\frac{GmM}{R^2}\hat{r}+\vec{F}_{missing}=\vec{0}$$ [here exists no centripetal force, but we added a missing term which make the net force to zero, for which we can provide the reason behind static earth]

Still, we've not considered that we are in a frame which is rotating with an angular velocity, and which is the reason we need to add an extra term the Centrifugal Force to study its motion also in a rotating frame.

$$\vec{F}_{missing}=m\vec{\omega}\times(\vec{\omega}\times \vec{R})=m\omega ^2 R \hat{r}$$ [Centrifugal force, a fictitious force]

Now,$$-\frac{GmM}{R^2}\hat{r}+m\omega ^2 R \hat{r}=\vec{0}$$

The Centrifugal Force doesn't exist, it needed to be considered when we are in an accelerating frame to study the motion.