# Centripetal and Centrifugal Acceleration.

I am a bit confused about these accelerations.

Anything that rotates has a linear acceleration which is a vector in the same direction as linear velocity . There is also a centripetal acceleration which "pulls" wants to pull the objects towards the axis of rotation. So the sum of these two vectors will be another total acceleration which will be equal to the square root of the sum of a linear and a angular . Therefore, if there is a body of mass m rotating about an axis,it would have a total force of m*(a total) which would always be perpendicular to the distance from the centre of rotation and thus explaining the circular motion.So if we are on a frictionless turntable rotating at a speed ω the centripetal acceleration will have no means (friction or tension )to keep us towards the centre and as a result we would follow the path of the tangential velocity ( V linear ).

What i cannot understand is what is a centrifugal force and how it is created and by whom .
Does it always exist in a circular motion just like the centripetal acceleration ?
My intuition whether it's true or not says that the centrifugal acceleration must always be smaller than the centripetal acceleration otherwise the resultant force would be directed outwards and instead of following the direction of the linear velocity we would "leave" at angle φ to it .

What about Newton's laws ? i thought they were always valid !

Doc Al
Mentor
I am a bit confused about these accelerations.

Anything that rotates has a linear acceleration which is a vector in the same direction as linear velocity . There is also a centripetal acceleration which "pulls" wants to pull the objects towards the axis of rotation. So the sum of these two vectors will be another total acceleration which will be equal to the square root of the sum of a linear and a angular . Therefore, if there is a body of mass m rotating about an axis,it would have a total force of m*(a total) which would always be perpendicular to the distance from the centre of rotation and thus explaining the circular motion.So if we are on a frictionless turntable rotating at a speed ω the centripetal acceleration will have no means (friction or tension )to keep us towards the centre and as a result we would follow the path of the tangential velocity ( V linear ).
If some mass is moving in a circle, it must have a radial (centripetal) component of acceleration. If it's also changing speed as it moves, it will have a tangential component of acceleration as well.
What i cannot understand is what is a centrifugal force and how it is created and by whom .
Does it always exist in a circular motion just like the centripetal acceleration ?
Centrifugal force is a 'fictitious' force (as opposed to a 'real' interaction force) that only appears when viewing things from a rotating reference frame. (Such 'forces' are also called pseudoforces or inertial forces.) As long as you stay with an inertial frame of reference, you won't need any such 'force'.
What about Newton's laws ? i thought they were always valid !
Newton's laws are valid in a non-accelerating, inertial frame. In order to apply them to accelerating frames, you must add various 'fictitious' forces to make things work out.

D H
Staff Emeritus
What i cannot understand is what is a centrifugal force and how it is created and by whom .
Does it always exist in a circular motion just like the centripetal acceleration ?
Centrifugal force is something that exists only in the eye of the beholder.

Think of a hammer throw. From the perspective of someone watching the event, the hammer thrower and the hammer are rotating about one another. There's a tension on the line that is responsible for the circular motion of the hammer. This force is directed inward; it's a centripetal force. There is no centrifugal force from this point of view.

Now think of what the hammer thrower sees. From his perspective, the hammer is not undergoing circular motion. It is instead just hanging there, motionless, right there in front of him. That tension on the line still exists. So how to explain that the hammer isn't moving? Simple: Invent a fictitious force that counters the centripetal force.

Note that there are no centrifugal forces in inertial frames of reference. They are a device that makes Newton's first two laws applicable in non-inertial frames.

Thank you very much !

"Note that there are no centrifugal forces in inertial frames of reference. They are a device that makes Newton's first two laws applicable in non-inertial frames." What do you mean by that ? ( English is not my first language).

haruspex
Homework Helper
Gold Member
2020 Award
Thank you very much !

"Note that there are no centrifugal forces in inertial frames of reference. They are a device that makes Newton's first two laws applicable in non-inertial frames." What do you mean by that ? ( English is not my first language).

An inertial frame is a frame of reference which is not itself undergoing acceleration.
Two inertial frames may be moving relative to each other, but only with constant relative velocity. Physics experiments conducted in two such frames should arrive at the same conclusions.
Accelerating reference frames (including rotating ones) can lead to curious results. E.g. Foucault's pendulum - if you thought the Earth was not rotating you'd have trouble explaining the pendulum's precession.

tiny-tim
Homework Helper
Hi ZxcvbnM2000! ZxcvbnM2000 said:
So the centrifugal force is a fictitious force that is felt only when you are in the centre of rotation and it only exists so that the Newton's Laws of motion can be valid.So an outside observer you not experience this force.

What we think is a centrifugal force if we are at the centre of rotation is actually the resistance of the body to changes in velocity , so what i am saying is that in reality what we call centrifugal force opposite and equal to the centripetal force is really a tangential force equal to m*alinear , right ?

you usually aren't at the centre

the classic case is you're in a car moving in a circle, clockwise say

in the frame of the car, there is a centrifugal force to the left …

if your seat was frictionless, you would slide left …

if there's friction, the friction force (to the right) balances the centrifugal force​

in a stationary frame, there's only friction …

the friction force (to the right) equals the centripetal acceleration times the mass That's how a washing mashine works , the wheel spins and the water is resisting to the continuous change in motion , so if it's spinning fast enough it will travel in a straight line and get out from the holes .

So how artificial gravity works ? I watched this video

22:40 - 32:00 . And i am really confused .

"the water is resisting to the continuous change in motion" … what does that mean? in the frame of a "car" spinning with the wheel, the water will slide sideways off the seat because of the centrifugal force

(and there's no video attached )

http://ocw.mit.edu/courses/physics/...mechanics-fall-1999/video-lectures/lecture-5/ :p

"the water is resisting to the continuous change in motion" … what does that mean?

If you are in a car and you are moving fast , if you hit the brakes then your body will move forward because it wants to keep going forward , it doesn't want to change .

In circular motion the mass wants to keep moving in a fixed direction but this doesn't happen because the velocity is changing the whole time so that's the " true centrifugal" force .

tiny-tim
Homework Helper
"the water is resisting to the continuous change in motion" … what does that mean?

If you are in a car and you are moving fast , if you hit the brakes then your body will move forward because it wants to keep going forward , it doesn't want to change .

oh i see …

yes, the water doesn't want to change but that's not "resisting the continuous change in motion" (of the car or of the wheel), it's ignoring it! In circular motion the mass wants to keep moving in a fixed direction but this doesn't happen because the velocity is changing the whole time so that's the " true centrifugal" force .

which frame are you in now? i don't think that explanation works in either frame

Cleonis
Gold Member
What i cannot understand is what is a centrifugal force and how it is created and by whom .
[...]
My intuition whether it's true or not says that the centrifugal acceleration must always be smaller than the centripetal acceleration [...]

You are mentioning two different things:
- centrifugal force
- centrifugal acceleration

That's two different things.

Now, let's look at some forces.
Let's say you are running along, and you use a sturdy pole to help you make a very fast U-turn. As you are about to pass the pole at arms length you extend your arm, you grab the pole, and you swing around 180 degrees.

In that situation, you provide the required centripetal force yourself. The pole is rigid in the ground, the pole will not budge. So the exerted force acts as a centripetal force, rotating you 180 degrees around the pole. Or, for that matter, you may just hold on, and keep circling the pole.

Is there a centrifugal force involved? Well, clearly you are exerting a force in centrifugal direction upon the pole. But since that pole is anchored to the entire Earth there is no way you're gonna move it.

Here's the thing: the centripetal force, and the force-in-centrifugal-direction, are equal in strength. That's a physics principle. (Codified as Newton's third law of motion.)
The difference is that you are unattached, and the pole is anchored to the entire Earth. So there is centripetal acceleration in proportion to the centripetal force, but there is in the example I give no centrifugal acceleration.
One remark, the pole may bend a little, and you can attribute that bending to a force exerted upon the pole, a force in centrifugal direction

But now another example:
You team up with somebody, you hold hands and then you start circling each other, moving as fast as the two of you can, so that the two of you are both circling the common center of mass. That fast circling requires a lot of centripetal force; you have to maintain a strong grip. You are exerting a centripetal force upon your teammate, and your teammate is exerting a centripetal force upon you.

In that case there is no point in attributing any of the motion to some "centrifugal force".

A third example, now just linear accceleration.
You are standing upright, in a bus that is accelerating. You hold on to a pole in that bus. Since you grip the pole firmly the pole is exerting a force upon you, accelerating you. You are exerting the same force upon that pole, but since that pole is secured to that bus-as-a-whole, and the big tires of that bus grip the road, you are not gonna move that pole; that pole is moving you.

So it's always a case of a force pair, (as codified in the form of Newton's third law). The two forces of the force pair are equal in strength, as a matter of principle. It's just that the object that is not attached to anything else is the one that is accelerated.

Last edited:
Doc Al
Mentor
Is there a centrifugal force involved? Well, clearly you are exerting a force in centrifugal direction upon the pole. But since that pole is anchored to the entire Earth there is no way you're gonna move it.

Here's the thing: the centripetal force, and the force-in-centrifugal-direction, are equal in strength. That's a physics principle. (Codified as Newton's third law of motion.)
Please do not confuse your 'force-in-centrifugal-direction' with the standard centrifugal force that we've been talking about in this thread. What you are illustrating can be called the reactive centrifugal force (if you insist on giving it a name--I wouldn't), but that is a real interaction force that obeys Newton's 3rd law. On the other hand, the standard centrifugal force under discussion is a fictitious force that does not obey Newton's 3rd law.

thank you very much :) Much appreciated !

Cleonis
Gold Member
[...] What i cannot understand is what is a centrifugal force and how it is created and by whom. [...]

[...] the standard centrifugal force that we've been talking about in this thread. [...]

Indeed as the thread developed what the replies were about was the fictitious centrifugal force.

But the original question was quite un-specific, it referred to 'a centrifugal force'. The original question implied a notion of a force that is actually exerted. So I chose to concentrate on a force that is actually exerted, referring to it generally as 'a force-in-centrifugal direction'.