Is centrifugal force just an apparency, while centripetal force is a real force? - by Robert Riedel - Quora Question Review

This document contains a review of the answer by Steve Baker on the question in Quora: "Is centrifugal force just an apparency, while centripetal force is a real force?"
To order to read all the answers select: https://www.quora.com/Is-centrifugal-force-just-an-apparency-while-centripetal-force-is-a-real-force?

• The text in italics is copied from the article.
  
• Immediate followed by some comments
  

Contents

• 1. Answer Review

Reflection

• Reflection 1 - Question Review and understanding

1. Answer Review

Questions like these about centrifugal force appear over and over again on this platform. Many are clearly confused, and judging by the answers, even those chiming in also appear, in many cases, to also be confused. There are two common misconceptions that seem endemic:

1. Centrifugal force is real, and

2. Centrifugal force is a reaction force

Centrifugal force is always fictitious. It is never real. In a rotating system, the only real force being applied is centripetal force. Centrifugal force is also NOT a reaction force.

The folks on the amusement park ride pictured below seem to be experiencing a force that is pulling them outward. However, the only forces they are actually undergoing are the downward force of gravity and the tension on the cables pulling them upward and inward toward the center of rotation: a centripetal force.

Besides the downward force of gravity a force is required to rotate the caroussel. This force also takes cares that the swings plus its visitors are rotating.

In fact, the reason why these people appear to be lifted against the force of gravity is because of the upward pulling vector force applied by those cables. There is no outward centrifugal force.

I will explore the reasons why in this answer.

Unfortunately, when reading the other answers on this thread, a good number of them are incorrect at worse, and misleading at best. Don’t get me wrong, some of the answers are correct. But when wrong, even those who claim to have doctorates in physics seem to have joined in on the misconception bandwagon, and that seems to be a sad testament to the quality of physics education that they received. Sadly, with social media, one gets what he pays for, and academic credentials on this platform seem to be meaningless.

I think that the only way to properly answer a question like this is to go back to the basics and review Newton’s three Laws of Motion. Misunderstandings about what they mean and how they are applied seems to be the fertile ground from which every misconception about centrifugal force grows. Please bear with me as we revisit the foundational principles of motion and force. Later, I promise, I will explore why centrifugal force is entirely imaginary (and by imaginary I do mean someone imagined that it exists).

1.1. Newton’s First Law of Motion

All matter has mass, and mass has inertia.

Both matter and inertia require a clear definition. See also: Reflection 1 - Question Review and understanding

Everyone should be familiar with inertia.

That is a personal opinion.

It is the tendency of mass to resist a change in motion. We all encounter it when we try to push a car.

The concept 'resist a change in motion' is not clear.
The main reason why it can be different to push two objects with the same volume and material is friction.
Considering two objects, made from the same material and subject to the same friction, the largest of the two is the most difficult to move.

The damn thing just doesn’t want to move. This concept was formalized by Newton’s First Law of Motion: “an object’s motion will not change unless an [unbalanced] force acts upon it.” Inertia has two consequences, objects in motion don’t want to stop moving, and objects that are not moving don’t want to start moving.

Anyone who owns a motor vehicle has likely had to do this at least once [2].

Newton’s Laws of Motion are a cruel mistress!

The concept 'Inertia' is not clear

1.2. Newton’s Second Law of Motion

The very real consequence of Newton’s First Law, is that force is required to move an object or to change its motion.

Newton's First Law does not explain why a force is required to change the motion of an object. Newton's first law is a description of a physical process.

And the amount of force required to move an object depends on its mass. It’s pretty easy to throw a soccer ball. It’s a lot harder to throw a medicine ball. Newton formally defined the concept as “the acceleration of an object is proportional to the force applied and inversely proportional to the mass of the object.”

F = ma (Force equals mass times acceleration).

Force and inertia come into play in rotating systems. A circling object does not want to move in a circle because of inertia. It wants to go in a straight line. The reason it does not is because there is an inward (centripetal) force that continually alters its trajectory. A rotating object is undergoing continual acceleration due to centripetal force.

A rotating object experiences an inward force, not outward, and that inward force overcomes its inertia and continually alters its trajectory — accelerating it around the center of rotation: F = ma.[3]

1.3. Newton’s Third Law of Motion

Anyone who has been hit in the face with a ball has experienced inertia. From your perspective, the ball clearly exerted a force on your face. On the other hand, from the ball’s perspective, your face clearly exerted a force on the ball. That is the essence of Newton’s Third Law of Motion: “for every action, there is an equal and opposite reaction.” Some refer to this as the “reaction force.” But that is actually something of a misnomer. Which came first, the force of the ball on your face, or the force of your face on the ball? They happened at exactly the same time and it’s impossible to determine which the force is the reaction force, because they are interchangeable depending upon the frame of reference. A force was clearly exerted on the ball, since it bounced off your face. But from the perspective of the ball, your face bounced off the ball. But more to the point: take note that the force and the reaction force operate on two different objects: the ball exerted a force on your face, and your face exerted a force on the ball.

I will return to the notion a bit later, but the paragraph above is why centrifugal force can never be a reaction force.

1.4 Centrifugal Force Is Not Real — It’s Imaginary

When a child hops on a merry go round and spins it, they perceive a force they call centrifugal force. But in reality, that is not the force they are experiencing at all. What they experience is centripetal force trying to pull then toward the spinning axis at the center, and that force is why they move in a circle. If it weren’t for that force they would simply move off the merry go round in a direction tangental to the circumference of rotation. This is simply Newton’s Second Law of Motion in action. By hanging onto the merry go round, that child is continually being accelerated toward the center of motion, until they let go, and the force ceases to be applied.

Dizzy yet! That force you feel isn’t centrifugal — it’s centripetal.

We also experience the same thing when cornering in a car at high speed. We perceive a force that is pushing us toward the door, but in reality the only force being applied is the friction of our butt in the seat forcing us to change direction with the car. If it weren’t for the fact that we are somehow affixed to the interior of the cornering car, we would continue moving straight while the car moved away from us.

That “force” we feel when cornering is fictitious. What we are sensing is our body’s tendency to continue straight while the vehicle is cornering but because of centripetal force it cannot. That force causes our body to undergo acceleration toward the center (not outward).

If I were enclosed in a cylindrical rocket with a top and a bottom and not in contact with any part of far away from any gravitational influences, and suddenly the rocket engine at the bottom was ignited, I would perceive that the bottom of the cylinder is rapidly approaching. Am I moving? I certainly appear to be set in motion and accelerating toward the floor of my rocket by some unseen force. It should be clear that until I am actually in contact with the bottom of the cylinder that there is no force on me at all. In that cylinder I am under the influence of an imaginary force. And once I come in contact with the floor of the rocket, the only force that exists is the force of the engine pushing me and overcoming my inertia. The force I perceive pushing me toward the rocket floor is similar to centrifugal force.

These perceived forces that “appear” to arise in accelerating systems, like rockets, merry go rounds and vehicles, are referred to as fictitious, pseudo, imaginary or apparent forces. In every case a force is perceived, but it isn’t real. The terminology used to name these forces offers a clue as to their existence. Fictitious means fictional. Pseudo means false. Imaginary means it only exists in one’s mind. And apparent means it appears like a phantom, and like all phantoms, they are imaginary.

1.5 Centrifugal Force is Not A Reaction Force

If I were to spin a bucket on a string, I am applying centripetal force to the bucket. What is the reaction force? It cannot be centrifugal force since both centripetal force and the perceived centrifugal force are acting on the bucket, meaning the forces are balanced. If the forces on the bucket are balanced, then by Newton’s First Law there can be no change in motion. However, the bucket is clearly rotating about the center, so it must be undergoing acceleration and hence subject to an unbalanced force.

A common misconception is that centrifugal force is the reaction force described in Newton’s Third Law of Motion. It isn’t …

What then is the reaction force if it isn’t centrifugal?

Recall our discussion earlier about Newton’s Third Law. The ball exerts a force on the face, and the face exerts a force on the ball. When I spin a bucket, we are both being spun about our centers of mass. That implies is that I am exerting a centripetal force on the bucket, and the spinning bucket is exerting a centripetal force on me about our common center of mass. The action and reaction pair are acting on two separate objects, just like the ball hitting a face!

1.6 Reference Frames and Centrifugal Force

Frame of reference is an important consideration in physics. Newtonian mechanics (described by the three laws of motion we reviewed only works in inertial reference frames. An inertial reference frame is any frame of reference not undergoing acceleration. Informally, a frame of reference refers to an observer’s point of view. Formally, frame of reference is an abstract coordinate system that can be used to standardize computations about force and motion. That coordinate system may define a position in space and sometimes time or motion.

Two reference frames, one stationary and one undergoing acceleration (one is inertial and the other non-inertial)[6]

In an inertial reference frame, an object at rest will remain at rest if no outside force is acting on it. However, therein lies the rub. We do not live in an inertial reference frame. If I place a ball on a hill it will roll down the hill. We know it rolls intuitively because of gravity, but gravity is not something we can perceive with our eyes. Its an invisible force that we know exists because we experience it first hand.

On the other hand, were I to climb in a rocket ship far away from any of the gravitational influences of stars or planets, and then subject the rocket to acceleration by firing its engine, I would experience a force pinning me to the floor of the accelerating rocket that is indistinguishable from gravity. Einstein famously used a similar example in his Theory of Relativity as a thought experiment. This equivalence principle states that gravity and the force felt in an accelerating reference frame are indistinguishable.

Similarly, were I to place a ball on a rotating platform, it would roll off under the influence of another unseen force we call centrifugal force. Both the rotating platform or the accelerating rocket (or us reading this answer here) are in non-inertial reference frames, so how on earth do we apply Newtonian mechanics applicable to inertial references frames to anything in the real world?

Simple, we assume the reference frame is inertial and we invent fictitious forces like centrifugal force (and dare I say gravity) to explain why an object at rest in our reference frame moves when it simply should not! This notion gives rise to things like the Coriolis force that meteorologists use to explain weather here on Earth. Some other fictitious forces are rectilinear acceleration (which we examined using a rocket), and the Euler force.

In rotating systems, simply assuming that fictitious forces actually exist makes models in our non-inertial world far simpler than going through all the machinations Newtonian mechanics would require to explain why a centrifuge separates substances by density.

1.7 But Centrifugal Force Still Isn’t Real

While assuming that certain forces exist when explaining motion in non-inertial reference frames, such as the one we inhabit, they still are not real. As the name suggests, certain forces are imaginary — which means that someone dreamed them up. They are like the allegorical fairy tales filled with magic and monsters that people tell their children to simplify moral lessons. They are like the fiction Trump tells his followers to convince them that the election was stolen in order to keep the contributions flowing in!

Even though magical beings may make morality lessons simpler for children to understand, they don’t actually exist![8]

All of physics is based on models of reality, but the models are not reality. On the other hand, those models simplify the complexity of the real world into abstractions our feeble minds can visualize. While I can find no examples of anyone dying because they failed to recognize the difference between real and fictitious force, distinguishing the two seems important if one’s goal is to understand how the world works.

Interestingly enough, four century old Newtonian Mechanics explains just about everything we experience in the real world. While Einstein and others may have shown us that the picture Newton painted wasn’t complete, for those of us not circling the Earth as a GPS satellite, or traveling at light-speed or colliding into particles in an accelerator, its close enough. I would argue if classical physics is to be taught in schools it should be taught correctly. Educators and tutors chiming in on this platform ought to make damn sure that what they are writing is correct, and its clear many of them are confused about the subject matter. Sadly, their egos get in the way of anyone telling them that they have missed the mark. And that’s a crying shame. You don’t even get an ‘E’ for effort!

Footnotes

3.

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