# Centripetal and centrifugal force

• jishitha

#### jishitha

In circular motion why the centripetal and centrifugal not get cancelling. .?

In circular motion why the centripetal and centrifugal not get canceling. .?
If they act on the same object, and are of equal magnitude, they do cancel. That is the case in a rotating frame for every object at rest in that frame.

It depends which centrifugal force you mean. If you mean the force that is reactive to the centripetal force then yes (like two bodies connected by a string, the tension applies centripetal force and centrifugal force and these cancel). However if you mean the force that would cause an object to fly away if centripetal force was stopped then I don't believe these do cancel since they would be at right angles to one another? If they did cancel the object wouldn't accelerate?

It depends which centrifugal force you mean. If you mean the force that is reactive to the centripetal force then yes (like two bodies connected by a string, the tension applies centripetal force and centrifugal force and these cancel).
The reaction to a force never cancels that force, because it acts on a different object.

However if you mean the force that would cause an object to fly away if centripetal force was stopped then I don't believe these do cancel since they would be at right angles to one another?
No, centrifugal and centripetal are never at right angle to each other.

If they did cancel the object wouldn't accelerate?
That is correct, That's why in the frame where the mass moves on a circle (accelerates) there is no force that cancels the centripetal force.

In addition to what has been said already: in classical physics every force belongs to a force pair (the 3d law of Newton). So, the circular motion of for example a CD forces the plastic into centripetal acceleration; the corresponding internal centripetal and centrifugal forces are due to the plastic's inertial resistance against acceleration.

Those two forces compensate each other in a certain way, just like when you stretch a string; however it can be misleading to say that they cancel each other. For if they really canceled then a string could not be stretched - and a CD could not break! :tongue2:
- (enjoy )

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In addition to what has been said already: in classical physics every force belongs to a force pair (the 3d law of Newton).
That is only true for inertial frames of reference.

Those two forces compensate each other in a certain way,
They compensate each other in terms of the net force on an isolated system (momentum conservation). Since total net force on an isolated system is zero, all internal forces (momentum transfers) must "cancel". Unfortunately this often is confused with: "forces on an individual part of the system canceling each other".

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That is only true for inertial frames of reference.
The laws of Newton are not valid (or at least, not intended) for non-inertial frames*.
They compensate each other in terms of the net force on an isolated system (momentum conservation). Since total net force on an isolated system is zero, all internal forces (momentum transfers) must "cancel". Unfortunately this often is confused with: "forces on an individual part of the system canceling each other".
Thanks for the precision!

*Compare: Einstein called in 1905 what nowadays are called "inertial frames", "coordinate systems for which the equations of mechanics are valid". [improved translation mine]

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The laws of Newton are not valid (or at least, not intended) for non-inertial frames*.
The first two are. Only the the third (and thus momentum conservation) fails in non-inertial frames. But that is good enough for some applications.

The first two [laws of Newton] are [valid (or at least, intended) for non-inertial frames]. Only the the third (and thus momentum conservation) fails in non-inertial frames. But that is good enough for some applications.

Newton's first law:

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

In order to use that law wrt a rotating reference system, some introduce a fictitious force that is exerted by a non-existing cause. :uhh:

The Principia's Scholium clearly shows that this law was not intended for such (mis-)use:

"The causes by which true, and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist. Again, true motion suffers always some change from any force impressed upon, the moving body; but relative motion does not necessarily undergo any change by such forces.
[...]
The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion.
[..]"

- http://gravitee.tripod.com/definitions.htm (just press Cancel)

, some introduce a fictitious force that is exerted by a non-existing cause.
Your cause-philosophy is irrelevant to physics. It doesn't affect the quantitative results. Or do you see the "cause of the force" appearing somewhere in F=ma ?

In order to use that law wrt a rotating reference system, some introduce a fictitious force that is exerted by a non-existing cause. :uhh:
Two big problems here: Not some, lots. And not :uhh:,

Extending Newtonian mechanics to non-inertial reference frames is a very powerful technique. For example, I challenge you to explain the physics of the Earth's oceans and the Earth's atmosphere from the perspective of a non-accelerating, non-rotating frame of reference to the extent needed to model the tides and hurricanes to the accuracy obtained by using an accelerating and rotating frame of reference.

The Principia's Scholium clearly shows that this law was not intended for such (mis-)use:
That was over three hundred years ago. The sciences place much less emphasis on the "great works" than do the humanities. Those initial thoughts motivate rather than dictate in the sciences. The Newtonian physics of today is quite removed from the physics that Newton developed. Just because Newton thought that non-inertial frames were somehow invalid does not mean that we think that way today.

That was over three hundred years ago. The sciences place much less emphasis on the "great works" than do the humanities.
Some people seem to confuse physics with some kind of religion, where you have to study and exactly obey the wise words of some ancient prophet.

The Newtonian physics of today is quite removed from the physics that Newton developed.
Newton saw further by standing on the shoulders of giants, and others saw even further by standing on his.

Just because Newton thought that non-inertial frames were somehow invalid.
I don't even see him saying that in the quoted text, but it is ancient language. He seems to explain the difference between proper acceleration (which he calls "true motion") and coordinate acceleration (which he calls "relative motion"). If he actually means true vs. relative velocity (absolute motion) then his text is simply outdated.

Your cause-philosophy is irrelevant to physics. It doesn't affect the quantitative results. Or do you see the "cause of the force" appearing somewhere in F=ma ?

Please abstain from personal attacks; I referred to the field of applicability of Newton's laws as implied by him. Here you suggest that Newton's "cause-philosophy" as well as the Principia were irrelevant to physics; I beg to differ.

Moreover, it's a big error to think that equations may be used outside of their intended field of applicability. For example, do you see inside the Lorentz transformations the requirement that they should be only applied to "coordinate systems for which the equations of mechanics are valid"? As I already pointed out, that statement excludes inertial frames.

Two big problems here: Not some, lots. And not :uhh:,

Extending Newtonian mechanics to non-inertial reference frames is a very powerful technique. For example, I challenge you to explain the physics of the Earth's oceans and the Earth's atmosphere from the perspective of a non-accelerating, non-rotating frame of reference to the extent needed to model the tides and hurricanes to the accuracy obtained by using an accelerating and rotating frame of reference.
I have no definite opinion about that matter, except that so far I did not see such a proof of superiority, which makes me doubt it. Therefore I already planned to start a thread with a challenge to those who make such claims, so they can show it (and convince me!). I will start that topic soon, thanks for reminding me of it!
That was over three hundred years ago. The sciences place much less emphasis on the "great works" than do the humanities. Those initial thoughts motivate rather than dictate in the sciences. The Newtonian physics of today is quite removed from the physics that Newton developed. Just because Newton thought that non-inertial frames were somehow invalid does not mean that we think that way today.
I merely showed that the laws of Newton as intended by him are invalid for non-inertial frames, as his laws refer to forces that can be related to causes. That is what I understand "classical physics" to be about (not only about that of course). However, other definitions of classical physics sure do exist.

Anyway, please don't ascribe to Newton a philosophy to which he strongly objected; that is unethical.

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Sigh... there is so much confusion on this topic. Centripetal force and centrifugal force do not cancel. They cannot, because they don't even exist in the same frame. In fact, they are the same force in the sense that they are the force describing rotational motion, but have different forms because they are in different frames. Tie one end of a string to a can, hold the other end of the string and get it spinning in a circle. In the reference frame of my finger, there is one force (neglecting gravity and friction): the centripetal force of the string pointing towards my finger. That is why the can accelerates in a circle rather than going in a straight line; it feels a total non-zero force. There's nothing canceling. In the frame of the can, it sees itself as at rest, but because it is in a non-inertial rotating frame, it feels something. What it really feels is the fact that it is in a non-inertial rotating frame, but it feels a lot like a force pushing outwards to the can in his rest frame. So we pretend the he does feel a force outwards in his frame and call it the centrifugal force.

You can do a mathematical exercise that is very enlightening. Start with Newton's laws, apply them in an inertial frame to a rotating system, switch your coordinates so that the frame becomes that of the object rotating, and you end up with something that is not Newton's law (no surprise because we're not in an inertial frame anymore), it has a few extra pieces. But for the sake of visualization and mathematical nicety, we can pretend that the result is Newton's law if we pretend the extra pieces are forces: the centrifugal force, the coriolis force, etc. This actually has important practical applications: the Earth is a rotating frame, but because it is so big, to people on the Earth's surface, it appears that we are in a non-rotating inertial frame. So we see global wind patterns and ascribe the causes to the coriolis force and centripetal force, but in reality, the cause of this patterns is because the Earth is rotating.
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Here's a great starting point.[/URL]

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harrylin said:
I merely showed that the laws of Newton as intended by him are invalid for non-inertial frames, as his laws refer to forces that can be related to causes.
"Causes" is so vague it can mean anything. Newton meant interaction forces that obey his 3rd law, but his ideas where extended and generalized by others.
harrylin said:
However, other definitions of classical physics sure do exist.
Yeah, you might want to catch up on the 300 years that came after Newton.

Sigh... there is so much confusion on this topic.
Yeah, and you adding to it:

Centripetal force and centrifugal force do not cancel. They cannot, because they don't even exist in the same frame.
They both exist in the co-rotating frame and cancel each other in that frame,

In fact, they are the same force in the sense that...[more of 'not even wrong']
No they are not. Not in any sense.

[..] you might want to catch up on the 300 years that came after Newton.
Already done! Apart of classical optics (Maxwell based), see the discussions in the appropriate forums:
- General Physics
- Quantum Physics
- Special & General Relativity
(etc.)

I have no definite opinion about that matter, except that so far I did not see such a proof of superiority, which makes me doubt it. Therefore I already planned to start a thread with a challenge to those who make such claims, so they can show it (and convince me!). I will start that topic soon, thanks for reminding me of it! [..]

I started the topic "Are fictitious forces necessary to solve certain problems?":

Looking forward,
Harald

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The laws of Newton are not valid (or at least, not intended) for non-inertial frames*.

I think Newton did use the principle of equivalence in his Principia.

http://www.cpt.univ-mrs.fr/~rovelli/book.pdf, p42, footnote 19

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I think Newton did use the principle of equivalence in his Principia.

http://www.cpt.univ-mrs.fr/~rovelli/book.pdf, p42, footnote 19

Interesting, thanks!
Applying the weak equivalence principle for linear, parallel acceleration in a gravitational field (without introducing fictitious forces) is quite a different matter from relating the laws of physics to a rotating reference frame.
As I cited, it's commonly known that Newton's laws were intended for inertial frames (compare also the text to which footnote 19 relates and p.39 small text and for example http://en.wikipedia.org/wiki/Coriolis_effect and http://en.wikipedia.org/wiki/Newton's_laws_of_motion).

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Centripetal force is not a force but a criterion for circular motion.

Centrifugal force is a fictitious force (along with the Coriolis and Euler forces) that arises when you perform a coordinate transform into a rotating frame. Either you have the rotating frame and accept they exist, or have an inertial frame and disregard them.

In circular motion body doesn't "stay out there". It is in constant motion around its circular path. Because its velocity is constantly changing in direction, the body accelerates and is not in equilibrium. If there were an additional outward force(centrifugal force) that balanced inward force, the net force would be zero and the body would move in a straight line , not in circle. In an inertial frame of reference there is no such thing as centrifugal force.

In circular motion body doesn't "stay out there". It is in constant motion around its circular path. Because its velocity is constantly changing in direction, the body accelerates and is not in equilibrium. If there were an additional outward force(centrifugal force) that balanced inward force, the net force would be zero and the body would move in a straight line , not in circle. In an inertial frame of reference there is no such thing as centrifugal force.

See posts #5, 6, 7: those forces do not cancel each other inside the system as they work on different bodies - that's what Newton's third law is about.

If there were an additional outward force(centrifugal force) that balanced inward force, the net force would be zero
That is what happens in the co-rotating frame, where the object is at rest.

In an inertial frame of reference there is no such thing as centrifugal force.
In an inertial frame of reference there is no inertial centrifugal force on the object in circular motion. But there can be centrifugal interaction forces on other objects, exerted by the object in circular motion.