Can centripetal and centrigugal force act together?

[monty37]

can centripetal and centrigugal force act together?

 

[Doc Al]

can centripetal and centrigugal force act together?

Realize that in standard physics usage "centrifugal force" refers to a fictitious (or inertial) force that only appears as an artifact of viewing things from a rotating--and thus noninertial--reference frame.

To answer your question directly: Sure. Imagine a ball tied to a string being swung in a horizontal circle. There is of course a "centripetal" force on the ball being provided by the string tension. If viewed from a rotating frame in which the ball is at rest, then you'd also have a centrifugal force acting on the ball. (Note that nothing actually pushes the ball outward.)

 

[daniel_i_l]

Centrifugal force is an imaginary force that's felt by observers in a rotating frame.
The centripital force is the actual force that's causing the rotating movment. So a stationary observer in a rotating frame feels a centripital force towards the center of rotation and a centrifugal force in the opposite direction. The two cancel out which is why the observer is stationary in the rotating frame.

 

[jonjacson]

Realize that in standard physics usage "centrifugal force" refers to a fictitious (or inertial) force that only appears as an artifact of viewing things from a rotating--and thus noninertial--reference frame.

To answer your question directly: Sure. Imagine a ball tied to a string being swung in a horizontal circle. There is of course a "centripetal" force on the ball being provided by the string tension. If viewed from a rotating frame in which the ball is at rest, then you'd also have a centrifugal force acting on the ball. (Note that nothing actually pushes the ball outward.)

¿do you mean that in the rotating frame you have both accelerations?

Centrifugal force is an imaginary force that's felt by observers in a rotating frame.
The centripital force is the actual force that's causing the rotating movment. So a stationary observer in a rotating frame feels a centripital force towards the center of rotation and a centrifugal force in the opposite direction. The two cancel out which is why the observer is stationary in the rotating frame.

I don't agree with that , a stationary observer in a rotating frame doesn't feel a centripetal acceleration, he is at rest .

If the angular speed of the non inertial reference frame remains constant , these are the forces (in this non inertial frame):

-gravity

-normal, equal to the gravity force, so they cancel

- the friction force pushing inward at your feet

-the centrifugal pushing outward to your feet.

So the friction force is equal to the centrifugal (if you are at rest), and that means:

Friction force= mrw2 =centrifugal force

The net result is a=0, and as a consequence there is not centripetal acceleration.

¿do you agree?

---------------It is very useful to make these problem:

A mass is at rest respect to the laboratory frame, while a frictionless turntable rotates beneath it . In the turntable frame ¿what are the forces?. And verify F=ma.

 

[Doc Al]

¿do you mean that in the rotating frame you have both accelerations?

No. In the rotating frame the two forces (centripetal and centrifugal) cancel and the acceleration is zero.

I don't agree with that , a stationary observer in a rotating frame doesn't feel a centripetal acceleration, he is at rest .

Don't confuse centripetal acceleration with centripetal force. The centripetal force still exists in the rotating frame.

 

[jonjacson]

No. In the rotating frame the two forces (centripetal and centrifugal) cancel and the acceleration is zero.


Don't confuse centripetal acceleration with centripetal force. The centripetal force still exists in the rotating frame.

I don't understand that, ¿can you show me the mathematical expression of the centripetal force in the non inercial frame?.

 

[Doc Al]

I don't understand that, ¿can you show me the mathematical expression of the centripetal force in the non inercial frame?.

In the example I gave in post #2, the centripetal force--which equals mω²r--is provided by the string tension. That string tension exists regardless of the frame you use.

 

[jonjacson]

In the example I gave in post #2, the centripetal force--which equals mω²r--is provided by the string tension. That string tension exists regardless of the frame you use.

Okey, now everithing is clear(I think), I was talking of another system, without a string, simply a mass above a rotating disk, so in that case the friction is the centripetal force ( because points to the center of rotation), and in the case of the string the tension is the centripetal force, in both cases centripetal acceleration is cero because centrifugal force is of the same magnitude and opposite sense ¿do you agree?

Other question when you use mw2r, that w is the angular speed of the rotation frame not of the object because is at rest, ¿am I wrong?.

Finally, in the turntable problem, you have that the body is not at rest, it has a speed v, so it appears a coriolis force pointing to the center of the rotating frame, so now that coriolis force is the centripetal force, we have the centrifugal force like always (if r is not parallel to the angular speed vector), and the net result of these two forces (coriolis pointing inward, and centrifugal pointing outward) is a centripetal acceleration mv2/r, the same as in the inertial frame.

¿everything is ok?

 

[Doc Al]

Okey, now everithing is clear(I think), I was talking of another system, without a string, simply a mass above a rotating disk, so in that case the friction is the centripetal force ( because points to the center of rotation), and in the case of the string the tension is the centripetal force, in both cases centripetal acceleration is cero because centrifugal force is of the same magnitude and opposite sense ¿do you agree?

Sounds good.

Other question when you use mw2r, that w is the angular speed of the rotation frame not of the object because is at rest, ¿am I wrong?.

That's correct--ω is the rotational speed of the frame.

Finally, in the turntable problem, you have that the body is not at rest, it has a speed v, so it appears a coriolis force pointing to the center of the rotating frame, so now that coriolis force is the centripetal force, we have the centrifugal force like always (if r is not parallel to the angular speed vector), and the net result of these two forces (coriolis pointing inward, and centrifugal pointing outward) is a centripetal acceleration mv2/r, the same as in the inertial frame.

Right! In the turntable problem all forces are fictitious, since the centripetal acceleration itself is just an artifact of using a rotating frame.

 

[ruko]

can centripetal and centrigugal force act together?

Centrifugal force is fictitious. It does not exist. A centrifuge should be called an inertiafuge. The question in my opinion should read, "Can centripetal force and inertia act together?"

 

[jonjacson]

Sounds good.That's correct--ω is the rotational speed of the frame.Right! In the turntable problem all forces are fictitious, since the centripetal acceleration itself is just an artifact of using a rotating frame.

When I have seen your reply, I was happy because I had started to think that I understand this, but about the third point ¿did you mean centripetal or centrifugal?.

Please say centrifugal, this already seems a tricky game with words

 

[Doc Al]

When I have seen your reply, I was happy because I had started to think that I understand this, but about the third point ¿did you mean centripetal or centrifugal?.

Please say centrifugal, this already seems a tricky game with words

I meant centripetal--towards the center. As seen in the rotating frame, the mass execute circular motion and thus is centripetally accelerated. (I'm a bit confused by your question since you identified the acceleration as centripetal yourself in post #8.)

 

[Doc Al]

Centrifugal force is fictitious. It does not exist. A centrifuge should be called an inertiafuge. The question in my opinion should read, "Can centripetal force and inertia act together?"

Fictitious inertial forces--such as coriolis and centrifugal--are extremely useful when analyzing motion from a rotating frame.

 

[monty37]

my book has given the "stone tied to a string " case as an example of centrifugal force.
well,applying the same to engineering concepts ,a mass tied to a shaft undergoing rotary motion, the book says there is a centrifugal force acting ,but with respect to an observer outside there is also a centripetal force?so they need to balance each other out,right?

 

[Doc Al]

well,applying the same to engineering concepts ,a mass tied to a shaft undergoing rotary motion, the book says there is a centrifugal force acting ,but with respect to an observer outside there is also a centripetal force?so they need to balance each other out,right?

The shaft pulls the mass in a circle; the inward force it exerts can be called the centripetal force. Viewed from a rotating frame, you would have a fictitious centrifugal force acting outward on the mass. The two "forces" balance each other.

 

[jonjacson]

I meant centripetal--towards the center. As seen in the rotating frame, the mass execute circular motion and thus is centripetally accelerated. (I'm a bit confused by your question since you identified the acceleration as centripetal yourself in post #8.)

Yes the acceleration is centripetal in the rotating frame , but i did not understand why you said at the end of your sentence "since the centripetal acceleration itself is just an artifact of using rotating frame".

Because I think that you use the concept of centripetal acceleration in the inertial frames too, so it is not something artificial developed to understand rotational frames (like coriolis or centrifugal force).

Perhaps I didn't express it sufficiently clearly.

Sounds good.That's correct--ω is the rotational speed of the frame.Right! In the turntable problem all forces are fictitious, since the centripetal acceleration itself is just an artifact of using a rotating frame.

 

[Doc Al]

Yes the acceleration is centripetal in the rotating frame , but i did not understand why you said at the end of your sentence "since the centripetal acceleration itself is just an artifact of using rotating frame".

All I meant was that when viewed from an inertial frame, the mass is not accelerating at all and no net force acts on it.

 

[monty37]

that is what i thought,they balance out each other,but there is no mention of centripetal force in the book,it is being balanced differently.
can you apply the same balancing principle to planet rotation around the sun?

 

[Doc Al]

that is what i thought,they balance out each other,but there is no mention of centripetal force in the book,it is being balanced differently.

What book are you using? What force do they say balances the centrifugal force?

can you apply the same balancing principle to planet rotation around the sun?

Sure, if you wanted to view it from a rotating frame in which the planet is at rest. (Not clear why you would want to do that, though.)

 

[D H]

All I meant was that when viewed from an inertial frame, the mass is not accelerating at all and no net force acts on it.

Surely you meant a non-inertial frame, not an inertial frame. There is of course zero centrifugal force in an inertial frame.

 

[Doc Al]

Surely you meant a non-inertial frame, not an inertial frame.

No, I actually meant inertial frame. My comment referred to the "turntable" problem, in which the mass is stationary and suspended above a rotating turntable. Viewed from the rotating frame, the mass is centripetally accelerated, but from the inertial frame it is at rest.

There is of course zero centrifugal force in an inertial frame.

That's certainly true.

 

[monty37]

actually it is a theory of machines book ,where the topic is about the balancing of
rotary masses,so these are inertial masses and in order to balance this,another
mass in the same plane is being attached to the shaft,in the opposite direction.

 

[monty37]

so how do you conclude the nature of this force,as to where which acts,centripetal or centrifugal,i mean generally,as in books especially in engineering concepts,it is highly unclear.

 

[Doc Al]

so how do you conclude the nature of this force,as to where which acts,centripetal or centrifugal,i mean generally,as in books especially in engineering concepts,it is highly unclear.

I'm not sure what you're looking for. If something is moving in a circle, then there must be a net radial force pulling it in. That net force is called the centripetal force. Centrifugal force is a "fictitious" force that is only used when analyzing motion from a rotating frame.

If there is a specific statement or problem in your book that has you confused, perhaps you can scan those pages in so we can see it. (But I must admit, some books are confusing.)

 

[sophiecentaur]

If you are on a turntable you will experience a non-fictitious force on you and if you hold up a pendulum it will lean 'out' along a radius. I really can't see why people get so up themselves when this force is called centrifugal. It can be regarded as a reaction against the (somehow acceptable) centripetal force but, as it is there, and you can feel it, why do people get their knuckles rapped for naming it? It disappears as soon as you remove it's cause, of course.
It's only the same type of phenomenon as the force which is pushing up un your bum as you read this.

 

[Doc Al]

If you are on a turntable you will experience a non-fictitious force on you and if you hold up a pendulum it will lean 'out' along a radius. I really can't see why people get so up themselves when this force is called centrifugal.

Non-fictitious, a.k.a. "real", forces have agents. The centrifugal "force" has none, since it's just an artifact of analyzing things from a rotating frame. Just because you "feel" an outward force on you does not mean that there is one.

It can be regarded as a reaction against the (somehow acceptable) centripetal force but,

No it can't, unless you are using "reaction" in some loose, non-Newton's 3rd law sense. The centripetal force is acceptable because it is "real"--there really is something exerting an inward force on something moving in a circle.

as it is there, and you can feel it, why do people get their knuckles rapped for naming it? It disappears as soon as you remove it's cause, of course.

Real forces don't "disappear" when you change frames.

It's only the same type of phenomenon as the force which is pushing up un your bum as you read this.

The force pushing up on your butt is a real force between your chair and you. Nothing fictitious about it, and nothing to do with centrifugal force.

 

[sophiecentaur]

Ok if that's a recognised definition. But the upwards force on your bum is surely no more real; it stops when you take the floor away. And how about the equivalence principle? Gravity and acceleration are equivalent are they not?
I'm sure you are in league with Mr. Scales, from 1962.
;-)

 

[monty37]

when we stir tea,the dregs tend to get collected at the centre,but
it should settle at the corners,right,in accordance with centrifugal force?

 

[sophiecentaur]

There's fluid dynamics at work here so I don't think that argument is my cup of tea. Does it even hold water? It 'leaves' out some facts and it may be an (Earl) Grey area.
Sorry - I'll get my coat.

 

[D H]

But the upwards force on your bum is surely no more real; it stops when you take the floor away.

The floor and the force it exerts most certainly are real. Of course you can test the hypothesis that it isn't real by jumping off the top of a tall building.

And how about the equivalence principle? Gravity and acceleration are equivalent are they not?

Yes and no. A lot of people misinterpret the equivalence principle. The equivalence principle says that no local experiment can distinguish between free-falling through empty space versus free-falling in a gravitational field.

Suppose you are in an enclosed spaceship (elevator car in Einstein's formulation). You feel a force from the floor of the vehicle pushing up on you. The vehicle might be out in space firing its engines or it might be standing still on the surface of a planet. Ignoring that the planet's gravitational field is not uniform, there is no way that you can tell the difference between these two scenarios. Now suppose instead that the vehicle is not firing its thrusters and that you are floating around inside the vehicle. Is this the vehicle is in deep space, far from any gravitational source, or free-falling (e.g., in orbit) about some massive body? Once again, you cannot distinguish between these scenarios using only experiments conducted within the vehicle.

I'm sure you are in league with Mr. Scales, from 1962.
;-)

Ad hominem attacks, and particularly those of a non sequitur nature, do not make for a good argument.

 

[sophiecentaur]

Which 'homo' am I supposed to be attacking? Mr Scales was my hero! He taught Physics like no other could. And I wouldn't attack YOU - you might be bigger than me. ;) - and you are telling me to take a running jump off a tall building, too.

My point was that, at an early age, I was given all the arguments about things not 'flying off' due to centrifugal force - which I, of course, appreciate because it could mean a big misconception and a false prediction. BUT, there is a force, which can be felt and measured and it IS in the direction opposite to the centripetal force. Furthermore, the direction of motion, when the central force is removed, asymptotes towards the 'away' direction even if it starts off tangential. The force's realness or otherwise is at another level of sophistication and it just seems over precise to make too much of a thing of it. I just wonder how many of the teachers who have shouted and screamed about it have given it as much thought as this thread has.

 

[D H]

WMr Scales was my hero! He taught Physics like no other could.

How are we to know who your Mr. Scales was? I thought you were referring to Junius Scales, the only Mr. Scales I could find who did something noteworthy in the early 60s.

My point was that, at an early age, I was given all the arguments about things not 'flying off' due to centrifugal force - which I, of course, appreciate because it could mean a big misconception and a false prediction.

Teachers (and textbook authors) who centrifugal force to explain orbits are, in my opinion, doing an incredible disservice to their pupils. For one thing, that explanation typically goes side-by-side with a drawing of a planet/satellite moving in circular path around the Sun/Earth. That circular path implies that the teacher or author is looking at things from the perspective of an inertial frame of reference. There is *zero* centrifugal force in this frame. The only perspective from which a circular orbit has a centrifugal force that exactly opposes the gravitational force is a rotating frame of reference in which the planet/satellite is stationary.

For another thing, orbits in general are not circular. They are elliptical.

Here are nine elliptical orbits with the same semi-major axis, eccentricity = 0.1 to 0.9 in steps of 0.1, as viewed from the perspective of an inertial frame:

With this inertial perspective, the shapes are simple and well-known (ellipses that share a common focus, and in this case, share a common semi-major axis). The descriptions of the orbits are once again simple and well-known (Kepler's laws). The equations of motion are yet again simple and well-known (Newton's second law + Newton's law of gravitation).


Here are the same orbits, but this time viewed from the perspective of a frame rotating with the mean motion of these orbits:

With this rotating perspective, the shapes are complex (this family of curves may have a name, but I don't know what it is). The descriptions of the orbits are complex, as are the equations of motion (Newton's second law + Newton's law of gravitation + centrifugal force + coriolis force).

BUT, there is a force, which can be felt and measured and it IS in the direction opposite to the centripetal force.

There is no measurable centrifugal force. The centrifugal force, if there is one, depends on the frame in which the picture is drawn. Whether you want to call it "real" is one thing. That it is measurable is quite another. It isn't.

 

[sophiecentaur]

Did I ever say that orbits are explained using centrifugal force?
'My' centrifugal force is the one you feel when you are on a fairground ride. It's there - I have felt it.
'My' Mr Scales was also notable to all his students; Google doesn't know everything.

 

[D H]

'My' centrifugal force is the one you feel when you are on a fairground ride. It's there - I have felt it.

That's not a centrifugal force. You feeling a centripetal force on those fairground rides.

Think about it this way: You are going around in a circle on those rides. That means your acceleration vector is pointing toward the center of the circle. That in turn means some force directed toward the center of the circle is acting on you, and that is by definition a centripetal force.

 

[sophiecentaur]

I know very well that the seat of the ride is pushing me inwards. The sums are quite clear. But I FEEL a force pushing my soft bits towards my back- 'outwards'. That force is away from the centre. Centrifugal, in fact. It is there just as much as the force of the ground on my feet. They are both reaction forces due to an acceleration. Why is this such a big deal? I just give a force a name and people get twitchy.

 

[D H]

I know very well that the seat of the ride is pushing me inwards. The sums are quite clear. But I FEEL a force pushing my soft bits towards my back- 'outwards'. That force is away from the centre.

As you knew Mr. Scales back in 1962, I assume you also knew Mr. Dodge Charger with a 426 Hemi back in 1966. If not that, pick some other 1960s muscle car. Those muscle cars weren't all that great on winding roads, but on a straightaway, DANG! Step on the gas and those puppies not only made you feel a force pushing your soft bits towards the back, they made you feel a force pushing every single one of your bits toward the back -- and right through the seat.

(Nostalgia time: My best car ever was a 1967 Plymouth Satellite that I bought in 1977 for all of $400. Unfortunately, two years later some old lady in a VW Rabbit ran a red light and front-ended me. My tank totally demolished her rabbit, but her rabbit did manage to crack my radiator and twist my suspension. End of an era ...)

Back to the topic at hand: Those muscle cars made you feel your bits pushed to the back when you stepped on the gas and accelerated forward. The car accelerated most of you forward. Your soft bits however, are only loosely connected to the rest of you. Those soft bits maintained their original momentum for a short time while your not-so-soft bits accelerated with the car. That pushed-to-the-back feeling resulted from you being accelerated forward. What you felt from those muscle cars of yore is exactly analogous to what you feel on one of those fairground rides.

 

[sophiecentaur]

Sorry to hear about the Plymouth. Insurance companies just don't understand about emotional attachment. "Beyond economic repair" is a phrase which they often apply to priceless objects.
Look, we're only arguing about a name. Because of Newton 3 we can always say that these forces appear in pairs. Mostly, we only consider and name one of the pair and I agree that centrifugal force is not the way to go in explaining what makes things go in a curve.
My fave car was a Lotus Super Seven, which was a bit like a roller skate. It could do 0 - 60 in less than 6 seconds (soft bits and all) with a 1500 Ford Cosworth engine. It woudn't do more than 100 and even at that it was screaming. Great at traffic lights in town until some brute in a Corvette Stingray left me behind in a cloud of dust. Really cut me down to size - then I bought a Ford Escort. . . .

 

[A.T.]

But I FEEL a force pushing my soft bits towards my back- 'outwards'. That force is away from the centre. Centrifugal, in fact.

You don't feel forces directly. You feel deformations of your body. Theses deformations occur because the centripetal force is applied non-uniformly to parts of you body. So what you feel indirectly is the centripetal force, not the centrifugal force. You feel a force pushing your back inwards against your soft bits.

If the centripetal force is suddenly gone and you fly off tangentially, the centrifugal force in the rotating frame is still there and accelerates you away from the center, but you don't feel any load. This shows that you cannot feel the centrifugal force.

 

[sophiecentaur]

OK - say we've got a conker on a string, whirling around. There MUST be two forces on each element of the string, keeping it taught. Those constitute the 3law pair I'm talking about. The must both exist or the string would be slack.
Yes, 'everyone' (at least you and I) knows the conker will fly off tangentially. That's not the issue. If I am on the conker, that's the frame I'm interested in and I guess I can change my interest when the string is cut - but I'm not going to cut the string.

What would you call the force pulling outwards on the string, then? (Bearing in mind that it does exist and is directed away from the centre and it needs a name).
I don't think you realize that we are arguing about semantics and not Physics.

 

[Doc Al]

What would you call the force pulling outwards on the string, then? (Bearing in mind that it does exist and is directed away from the centre and it needs a name).

Why does every force need a special name? Note that you are talking about an outward force on the string, not on the object. (Viewed from a rotating frame, centrifugal force acts on the object.) The string and object exert forces on each other. If you want to call that force on the string something, don't call it the 'centrifugal force'--that term already has a specific meaning in physics. (Some use the term 'reactive centrifugal force'--use that at the risk of confusing people.)

 

[jambaugh]

so how do you conclude the nature of this force,as to where which acts,centripetal or centrifugal,i mean generally,as in books especially in engineering concepts,it is highly unclear.

I always kept them straight by remembering the 'f' in centrifugal stands for 'flee' so it is the apparent radial outward force in a rotating frame while a centripetal force is the force typically opposing the centrifugal and effecting the circular motion. (The latin root fugere means 'to flee' also use to define fugacity in thermodynamics.)

 

[D H]

What would you call the force pulling outwards on the string, then?

Tension.

I don't think you realize that we are arguing about semantics and not Physics.

Misusing names can lead to confusion. The term centrifugal force has a specific meaning.

 

[sophiecentaur]

Tension.

Doesn't tension operate in both directions in the string? I think that's a cop-out.

Misusing names can lead to confusion. The term centrifugal force has a specific meaning.

I guess that's the best argument against using it when it's not appropriate. So what can we call it? Tension is just not specific enough - because it doesn't describe the force of my body against the seat on the ride.

 

[rcgldr]

Wiki has updated it's "reactive centrifugal force" article:

http://en.wikipedia.org/wiki/Reactive_centrifugal_force

Perhaps it's not common usage in physics, but it is common usage in English, which is a larger audience, and I doubt the term centrifugal force is confusing to anyone in physics, who would know that it's a reactive force in a standard inertial frame.

 

[sophiecentaur]

So they now have "reactive centrifuges" in Biology labs? Fair enough. Do you think it will catch on?

 

[A.T.]

What would you call the force pulling outwards on the string, then? (Bearing in mind that it does exist and is directed away from the centre and it needs a name).

That is the reactive centrifugal force (a 'real' interaction force that exists in every frame):
http://en.wikipedia.org/wiki/Reactive_centrifugal_force

Not to be confused with centrifugal force (a 'fictional' inertial force that exists only in the rotating frame):
http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)

 

[rcgldr]

In some cases which forces are real or reactive get a bit fuzzy. Here is an example of a radio control glider dynamic soaring in circles at speeds up to 375 mph (the mentioned 392 mph pass wasn't caught on video):

http://www.youtube.com/watch?v=WaQB16ZaNI4&fmt=18

While circling, the air exerts a centripetal force on the glider, causing the glider to accelerate inwards, following a circular path. This coexists with the glder exerting a centrifugal force on the air, causing the air to accelerate outwards in a spiraling path. Here the glider's outwards reactive force coincides with the outward force the glider exerts onto the air, and the air's inwards reactive force coincides with the inwards force the air exerts onto the glider.

Similarly imagine a rocket in space void of gravitational effect, using it's thrust to follow a circular path. The spent fuel exerts a centripetal force on the rocket, causing the rocket to accelerate inwards, following a circular path. This coexists with the rocket exerting a centrifugal force on the spent fuel, causing the spent fuel to accelerate outwards in a spiraling path. Here the rocket's outwards reactive force coincides with the outward force the rocket exerts onto the spent fuel, and the spent fuel's inwards reactive force coincides with the inwards force the spent fuel exerts onto the rocket.

update - so which of the forces in these examples are "fictitious"?

 

[D H]

Stop that, Jeff!

 

[sganesh88]

Here the glider's outwards reactive force coincides with the outward force the glider exerts onto the air, and the air's inwards reactive force coincides with the inwards force the air exerts onto the glider.

They coincide because they are one and the same. Same is the case with the rocket example too. When you hit a wall, there is only one force exerted by you on the wall. You seem to think there are two- namely the force exerted by you on the wall and the reactive force you exert on the wall. This isn't true. We cannot absolutely classify a force as action or reaction. Its just that forces observed from an inertial frame occur in pairs of action and reaction.

so which of the forces in these examples are "fictitious"?

Terming a force as fictitious depends on the reference frame. If you have observed the above two events from an inertial frame, then all the forces you measure are real.

 

[jambaugh]

If you want to argue semantics then let's make it clear what the debate is.

*** In one context "centripetal" and "centrifugal" are just qualifiers for resp. negative radial and positive radial directions and you can also speak of centripetal velocity or centrifugal displacements as well as further qualify with "reactive" or "applied" or whatever. In such context the two words are redundant (which isn't necessarily bad) as we could as easily speak of positive centrifugal and negative centrifugal or similarly negative centripetal and positive centripetal.

*** In another context we resolve the vector acceleration of a particle in polar coordinates:

\vec{a}= \ddot{\vec{r}} = (\ddot{r}-r\omega^2) \hat{r} + (r\dot{\omega} +2\dot{r}\omega)\hat{\theta}
(\omega = \dot{\theta})

We get two sets of terms.

The coordinate accelerations:
\vec{a}_{cord}= \ddot{r}\hat{r} + r\dot{\omega}\hat{\theta}
and the components emerging from rates of change of our basis (local frame):
\vec{a}_{frame} = -r\omega^2 \hat{r} + 2\dot{r}\omega\hat{\theta}

We can then express Newton's 2nd law in two forms:
\vec{F} = m\vec{a}
or
\vec{F}_{eff} = m\vec{a}_{coord}
where the l.h.s. is an "effective force" which is the "physical force"
plus the "pseudo-forces" or "fictional forces" we get by subtracting out mass times the frame accelerations.

They are the coriolis force:
\vec{F}_{cori}= -2m\dot{r}\omega\hat{\theta}
and the centrifugal force:
\vec{F}_{cnf} = mr\omega^2\hat{r}

Now when considering systems where the coordinate acceleration is zero the centrifugal force must be canceled by a radial component of the "physical force" which component we call the "centripetal force".

*** Now we can also adopt a third context not totally distinct from the second one wherein we consider a uniformly rotating frame which itself may be resolved in rectangular or polar coordinates or some nastier system. We may even use an origin distinct from the center of rotation. In this context when using non-rectangular coordinates we will again need to resolve out coordinate and "local frame" components of acceleration while also taking into account the effects of the over-all time dependency of the rotating coordinate system.

It is thus useful (and consistent with Einstein's equivalence principle) to treat the coriolis and centrifugal forces due to the global frame rotation as "physical" e.g. a form of gravity. We will also have as before local frame components of the acceleration which we can again refer to as "pseudo-forces" if that is our inclination.

Typical examples in this last context are ballistics and the dynamics of a hurricane given the rotation of the Earth.

Now I think it is silly to argue over "fictitious" vs. "real" forces especially given GR where all gravitational forces are just as "fictitious" as the coriolis and centrifugal ones here. The important point is correct bookkeeping. We must be sure that Newton's 2nd law (F - ma =0) gets transformed correctly when we change coordinate systems.

Personally I am for dropping the "fictitious" or "pseudo" qualifiers in physics. (Though they may still be appropriate in engineering.) We should properly recognize that Einstein's equivalence principle goes both ways and such distinctions are meaningless. After all in Kaluza-Klein theory EM forces end up being "fictitious" as well. Consider also covariant momenta and gauge transformations when we define forces as rates of change of momenta.