# Exploring the Mathematical Application of Centrifugal Force

In summary, the centrifugal force is not a real force, but it can be used mathematically. Newton's first, second and third laws still apply in a rotating coordinate system. The centrifugal force is used to create artificial gravity in spacecraft.
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We all know that the Centrifugal force is not a real force.However,we can use it mathematically.
This Wikipedia Article on Centrifugal force
States that:
The concept of centrifugal force is applied in rotating devices such as centrifuges, centrifugal pumps, centrifugal governors, centrifugal clutches, etc., as well as in centrifugal railways, planetary orbits, banked curves, etc. These devices and situations can be analyzed either in terms of the fictitious force in the rotating coordinate system of the motion relative to a center, or in terms of the centripetal and reactive centrifugal forces seen from a non-rotating frame of reference; these different forces are equal in magnitude, but centrifugal and reactive centrifugal forces are opposite in direction to the centripetal force.
But,

According to Newton's first law,objects tend to move in a straight line or stay at rest at a constant velocity unless no external force is acted.
The Centrifugal force should act on the velocity direction.If so,Why does the wikipedia article says this.
Moreover,There have been many ideas of artificial Gravity using centrifugal force.(So,in favor of wikipedia article)

Whatever the Wikipedia,My question is why does not the force act at velocity direction?

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The centrifugal force is actually Newton's first law, centripetal and centrifugal force's act opposite to each other because the ball is trying to go straight, not go around in a circle. In the reference frame of the circle, that straight line is like a force. The forces balance and result in a velocity perpendicular to them.

And remember, the tangential velocity is not increasing, so there's no reason there should be acceleration (i.e. force) in the direction of the ball's motion.

1 person
To avoid confusion, I suggest you forget about "centrifugal force" (because, as you said, it is not a real force) until you thoroughly understand how circular motion at constant speed (or constant angular velocity, which is the same thing) is caused by a real (centripetal) force and Newton's laws of motion.

Remember that Newton's laws of motion are only valid in an inertial reference frame, or coordinate system - i.e. one that is not rotating. "Centrifugal force" (and also the Coriolis force) are just extra terms added to Newton's "F = ma" equation, to make the math work in a coordinate system rotating at constant angular velocity. They are not physical forces.

And as for "reactive centrifugal force" mentioned in your quote from Wiki, I have said before on PF that IMO anybody using that term as if it meant something should be put before a firing squad. I have never seen it in any peer reviewed literature, the Wiki reference to it in a book published in the 19th century is irrelevant in the 21st century, and every website I have seen that uses it appears to be quoting the wiki page, with or without acknowledgment.

The force you feel that causes "artificial gravity" in a rotating spacecraft is just the real centripetal force that is accelerating you towards the center of rotation. The only difference between this and a mass on a string, is that the string is pulling on the mass from "inside" its circular orbit, but the space station is pushing on your feet from "outside". Both forces act in the same direction - towards the center of rotation.

If a real force acts along the tangent to the circle, it changes the speed of the object. The only possible direction a force can act which does not change the speed is perpendicular to the velocity vector, and the centripetal force (towards the center of the circle) is perpendicular to the velocity.

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1 person
According to Newton's first law,objects tend to move in a straight line or stay at rest at a constant velocity unless no external force is acted. The Centrifugal force should act on the velocity direction. If so, why does the wikipedia article says this.
Netwon third law pair of forces do not act on the same object, these are the forces that two objects exert on each other. The inertial frame "reactive centrifugal force" is the force the object exerts on the end of the string in reaction to centripetal acceleration coexisting with the string exerting a centripetal force on the object. The object only experiences a centripetal force, so it's speed remains constant, and only it's direction changes. The string experiences two forces, the "reactive centrifugal force" exerted by the object at the end of the string, and an inwards force holding the string in place at the center, so the string is under tension. If the string was massless, then the tension would be the same at all points within the string.

1 person
1-What force makes the ball go perpendicular to the direction of centripetal force?

First a force should make the ball move in that direction.Only then centripetal force only can change it's direction.
Am I wrong?

1-What force makes the ball go perpendicular to the direction of centripetal force?

First a force should make the ball move in that direction.Only then centripetal force only can change it's direction.
Am I wrong?
No, you're not wrong. But it's irrelevant here. It is asumed the ball already has got some velocity. Whatever force made the ball move at some time in the past, is now gone.
Since it already does, the ball will keep moving with constant speed and direction unless some force acts on it. And unless there's some component of the force that is NOT exactly perpendicular to the direction it moves, it will not change its magnitude.

1 person
I see.All my questions are now answered.Thank you all

400th yay

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AlephZero said:
And as for "reactive centrifugal force" mentioned in your quote from Wiki, I have said before on PF that IMO anybody using that term as if it meant something should be put before a firing squad. I have never seen it in any peer reviewed literature, the Wiki reference to it in a book published in the 19th century is irrelevant in the 21st century, and every website I have seen that uses it appears to be quoting the wiki page, with or without acknowledgment.

Well said. I agree completely.

AM

AlephZero said:
And as for "reactive centrifugal force" mentioned in your quote from Wiki, I have said before on PF that IMO anybody using that term as if it meant something should be put before a firing squad. I have never seen it in any peer reviewed literature, the Wiki reference to it in a book published in the 19th century is irrelevant in the 21st century, and every website I have seen that uses it appears to be quoting the wiki page, with or without acknowledgment.

A.T. said:
The objection is not to the contention that a centripetal force has a "reaction" force as required by Newton's third law. The problem is really with the confusion and misinformation surrounding this term as illustrated by many of the "authorities" that your google link points to. That is probably why reputable physics texts avoid the term.

The links provided illustrate the point that AlephZero made. Which ones qualify as peer reviewed literature?

The first link is to what appears to be a high school textbook which states:

"It is important to note that centrifugal reaction is not centrifugal force. Centrifugal reaction is a reaction force according to Newton's third law of motion, whereas centrifugal force is a pseudo force in a non-inertial frame."​

Does anyone here think that this explanation means anything let alone anything that will help the student understand the physics of circular motion?

There is a link http://www.mathpages.com/home/kmath633/kmath633.htm talks about the repulsive force between two electrons approaching each other as a "centrifugal reaction" force. The drawing shows non-existent centripetal and centrifugal forces that can only cause confusion to a student and anyone trying to learn about centripetal forces.

The authority cited in the Wikipedia article, "www.books.google.ca/books?id=QnJqIyk_dzIC&pg=PA47&dq=%22reactive+centrifugal+force%22&lr=&as_brr=0&sig=EDmHHDZRZB4AC37tklWe03SD_tY&redir_esc=y#v=onepage&q=%22reactive%20centrifugal%20force%22&f=false" uses an example that is simply wrong:

"Similarly the sun will feel such a reactive, centrifugal force from each of the planets that it holds in an orbit by its force of gravity."​

AM

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We are not rehashing this for the hundredth time.

## 1. What is centrifugal force?

Centrifugal force is the outward force that is experienced by an object moving in a circular path due to its inertia.

## 2. How is centrifugal force calculated?

Centrifugal force can be calculated using the formula F = mv²/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.

## 3. What is the difference between centrifugal force and centripetal force?

Centrifugal force is the outward force experienced by an object, while centripetal force is the inward force that keeps an object moving in a circular path.

## 4. Can centrifugal force be greater than gravity?

No, centrifugal force cannot be greater than gravity as it is a fictitious force that only appears to exist due to the circular motion of the object.

## 5. How does centrifugal force affect everyday objects?

Centrifugal force can affect everyday objects in various ways, such as causing liquids to move to the outer edge of a spinning container, or causing objects on a merry-go-round to feel like they are being pushed outwards.

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