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Centrifugal force

by asi123
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D H
#55
Jun30-08, 01:28 PM
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A science fiction setting:

Two fiercely competitive species find an airless, spinning planet chock full of metals. Each builds an armed mining outpost, only to discover the other species has also found the planet. One species fires first, consistently missing their enemy. The commander asks the science officer whether the firing system models the Coriolis force. The science officer says it's not modeled and won't budge when told to incorporate it because "It's not a real force". The commanding officer finds another solution: Make the guns aim at where the enemy outpost will be when the missiles hit rather than where it is when the missiles are launched. The science officer agrees to this, but says that this will take some time.

Meanwhile, the other species retaliate. They come from a rapidly spinning world and have the Coriolis force factored in. It doesn't matter to them that the force is not real; the effect is real. Their guns are deadly accurate.

========================================================

All of this debate on whether the centrifugal and Coriolis effects are "real" misses the mark. Hurricanes form because of the Coriolis effect, and gravity varies with latitude in part because of the centrifugal force. These very real effects are explainable without the aid of fictitious forces from the point of view of an inertial observer. Sometimes an inertial perspective happens to be extremely inconvenient. Atmospheric modeling is one such example.
rcgldr
#56
Jun30-08, 01:48 PM
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Quote Quote by Doc Al View Post
Anyone using "centrifugal force" to mean a real, reactive force--instead of the standard definition as a "fictitious" force--should add a disclaimer in bold red letters: This is not standard physics usage--read at your own risk!
Well maybe you should update or delete the wiki reference to "reactive centrifugal force".

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

I for one prefer to use non rotational, non accelerating frame of references, and centrifugal force should have a meaning in a more common frame of reference.

Getting back to that person that is twirling an object, what do you call the outwards and rotating force that person applies at the contact patch between his feet and the ground (either a platorm on a frictionless plane, or the earth)?
Doc Al
#57
Jun30-08, 02:01 PM
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Quote Quote by Jeff Reid View Post
Well maybe you should update or delete the wiki reference to "reactive centrifugal force".
In general, I would not use Wiki as a serious reference. Pick up any intermediate classical mechanics textbook instead.

I for one prefer to use non rotational, non accelerating frame of references, and centrifugal force should have a meaning in a more common frame of reference.
Use a different word then. But don't use a word that already has a standard meaning in a nonstandard way. (And try analyzing large scale atmospheric effects from an inertial frame--good luck!)

Getting back to that person that is twirling an object, what do you call the outwards and rotating force that person applies at the contact patch between his feet and the ground (either a platorm on a frictionless plane, or the earth)?
Why does it need a special name? You twirl a rock on a string, the string pulls on you, you pull back on the string. (I'd call those forces string tension.) The ground exerts a friction force on you to prevent slipping (and you, of course, exert an equal and opposite friction force on the ground).
cabraham
#58
Jun30-08, 02:39 PM
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So it appears to be that we agree that centrifugal is a fictitious or virtual force created to balance centripetal in a specific ref frame. I still take issue with those who say Coriolis is not a real force. My understanding is as follows.

If we regard earth as a ref frame and wish to fire a projectile from the equator northward, we must account for rotation of the earth. When the projectile is fired, it has the velocity eastward equal to that at the equator. As it traverses its path northward, it maintains its eastward linear velocity while the earth underneath maintains its eastward angular velocity. When the missile lands north of the equator, its eastward velocity is greater than the eastard *linear* velocity of that spot on earth north of the equator. Hence the missile lands *east* of its intended target spot had Coriolis not been accounted for.

I've always regarded Coriolis as a "correction term" that must be computed to account for the above phenomenon. While the missile is airborn, of course there is no literal "Coriolis force" acting on it to accelerate it eastwardly. From the earth ref frame, if we treated the earth as stationary then the missile won't land where we thought it should have. What "knocked the missile off course?" We add the Coriolis term as a correcting factor. The Coriolis component is not an actual force acting on the airborn missile deviating its path. Rather it is a correction term accounting for the fact that a rotating ref frame cannot be equated to a stationary one.

There is no literal Coriolis force actively influencing the missile trajectory, but rather it is a correction term accounting for the deviation AS IF THERE WAS a "real" Coriolis force. The force is not literal, but the missile's path deviation is absolutely real. Coriolis force is a virtual force mathematically defined to account for A VERY REAL NON-FICTITIUOS path deviation.

That's my understanding of the "Coriolis component" using my undergrad physics prof Dr. M terminology. Dr. M knew his stuff. In 3 decades of EE R & D, his teachings never once failed me. He was brilliant. Dr. M, wherever you are, "you da man!"
cmos
#59
Jun30-08, 02:48 PM
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cabraham,

That's exactly why it is a fictious force. It is manifested only to correct for the fact that your frame of reference is non-inertial.

In firing a projectile (such as a missile) over long distances over the Earth surface, the Coriolis force will play a significant role. This is the non-inertial view.

But if your launch center was from a point in space, you wouldn't have to worry about the Coriolis force; you'd just have to account for the fact that you are firing at a moving target (the Earth). This is the inertial view.
D H
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Jun30-08, 03:35 PM
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Quote Quote by cabraham View Post
The force is not literal, but the missile's path deviation is absolutely real. Coriolis force is a virtual force mathematically defined to account for A VERY REAL NON-FICTITIUOS path deviation.
Bingo! The Coriolis force is a fictitious force. When viewed by an inertial observer, a balistic missile flies in a plane. There is no curvature of the path.

There is an easy test of whether a force is real or fictitious: Can you build a black box to measure the force? Fictitious forces arise from the observer's perspective rather than from some real force that truly does act on the body. Can we measure the normal force? Sure. You step on a scale every morning. Can we measure tension? Sure. Can we measure a centrifugal force or Coriolis force: Nope. These are observer-dependent. They aren't real.

One such measuring device is an accelerometer. The Newtonian view of a perfect accelerometer is a device that measures all real forces except gravitation acting on some body. Why that "except gravitation" clause? The GR view is "A perfect accelerometer is a device that measures all real forces acting on some body, period. There is no reason to exclude gravity because gravity is not a real force."
tiny-tim
#61
Jun30-08, 06:41 PM
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Quote Quote by D H View Post
FYI Cabraham, tiny tim is a PhD physics candidate.
Who me??

I'm just a little goldfish who tries to make three-dimensional sense out of the two-dimensional images I see projected onto the boundary of the bowliverse.

oooh I've just thought of a question
forces do work
can centrifugal force do work?
rcgldr
#62
Jun30-08, 08:20 PM
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So when are they going to change the name of a centrifuge to a centripuge?
George Jones
#63
Jul1-08, 07:33 AM
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Quote Quote by tiny-tim View Post
Who me??

I'm just a little goldfish who tries to make three-dimensional sense out of the two-dimensional images I see projected onto the boundary of the bowliverse.

oooh I've just thought of a question
forces do work
can centrifugal force do work?
I can't recall running into this, but it seems to me that work in non-inertial frames can be useful. For example, I think the work-energy theorem can be used to find a particle's change in speed in a non-inertial frame.

Still don't have time to respond like I want; on my out the door again.

I am going to need a vacation to recover from my current vacation at my in-laws!
cmos
#64
Jul1-08, 09:33 AM
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Quote Quote by tiny-tim View Post
oooh I've just thought of a question
forces do work
can centrifugal force do work?
Good question!


It seems counter-intuitive to me, but I want to say yes. Consider a particle placed on a rotating disc. The centrifugal force on the particle is
[tex]\vec{F}_{cent}=m\omega^2\vec{r}[/tex]
where r is directed radially. So in a particle being pushed from a point near the axis towards the edge of the disc, work must be performed:
[tex]W=\int \vec{F}_{cent} \bullet d\vec{r} [/tex]


My problem with this is where does the work go in the inertial frame? Also, clearly the Coriolis force cannot do work:
[tex]\vec{F}_{Cor}=-2m \vec{\omega} \times \vec{\dot r}[/tex]
where dr/dt is the velocity of the particle in the non-inertial frame. So I find it an oddity that one fictious force may do work while another may not.
George Jones
#65
Jul1-08, 10:34 AM
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Quote Quote by cmos View Post
My problem with this is where does the work go in the inertial frame?
When considering work, usually only one frame is used. Even when restricted to inertial reference frames, a force can do zero work in one frame and non-zero work in another.

Consider the following example.

In an inertial frame, a particle is subject to a (net) force. Suppose that when the force starts acting, the velocity of the the particle is [itex]c \hat{e_1}[/itex], and that the velocity of the particle when the force stops acting is [itex]c \hat{e_2}[/itex], where [itex]c[/itex] is a constant. Because the initial and final speeds are the same, there is no change in kinetic energy, and, by the work-energy theorem, no work done on the particle by the force.

Now consider the same situation from the point of view of an inertial reference frame that moves with velocity [itex]c \hat{e_1}[/itex] with respect to the first inertial reference frame. In this frame, the initial velocity of the the particle is [itex]\vec{0}[/itex], and the final velocity of the particle is [itex]c \left( \hat{e_2} - \hat{e_1} \right)[/itex]. In this frame, the change in kinetic energy and work done is [itex]m c^2[/itex].

Also, clearly the Coriolis force cannot do work:
[tex]\vec{F}_{Cor}=-2m \vec{\omega} \times \vec{\dot r}[/tex]
where dr/dt is the velocity of the particle in the non-inertial frame. So I find it an oddity that one fictious force may do work while another may not.
A "force" of this form can change the direction of a particle's motion, but cannot change a particle's speed. Again, this is true in both inertial and non-inertial frames. For example, a moving charged particle in a "real" magnetic field is subject to a force (proportional to) [itex]\vec{v} \times \vec{B}[/itex], which does no work.
cmos
#66
Jul1-08, 12:30 PM
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Excellent! Thank you for the very clear explanation. Bravo, Prof. Jones.
rcgldr
#67
Jul1-08, 05:01 PM
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Quote Quote by tiny-tim View Post
Can centrifugal force do work?
Take the example of the person twirling an object. Change this to a person holding a very low friction pipe with a string going through it. The are objects attached to both ends of the string. The person twirls one of the objects, and the rotating object reacts to the centripetal force from the string by applying a "reactive centrifugal force" to the string, creating a tension, which in turn can lift the object dangling below the pipe at the other end of the string.

Work done is peformed on the hanging object, it's weight times the height the hanging object is raised.

Work is also done on the rotating object by the person, equal to it's change in kinetic energy.

Quote Quote by George Jones View Post
Even when restricted to inertial reference frames, a force can do zero work in one frame and non-zero work in another.
Rockets in space and thier spent fuel are a good exception. Assume an environment with no external forces (free of gravity). Momentum is preserved. All the work done is internal, and increases the kinetic energy of fuel and/or rocket, depending on the reference frame, but it will turn out that, within reason, the frame of reference won't change the amount of work done, since it's source the the chemical energy of the fuel. Even if the frame of reference is the accelerating rocket itself, all the work is done to the fuel in this frame of reference, but it's the same amount of work done as observed in constant velocity frame of reference.
George Jones
#68
Jul1-08, 06:13 PM
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Quote Quote by Jeff Reid View Post
The person twirls one of the objects, and the rotating object reacts to the centripetal force from the string by applying a "reactive centrifugal force" to the string, creating a tension, which in turn can lift the object dangling below the pipe at the other end of the string.
As`Doc Al already said in post #54, reactive centrifugal force" is very non-standard terminology in physics.
George Jones
#69
Jul2-08, 07:27 AM
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Quote Quote by cmos View Post
Excellent! Thank you for the very clear explanation. Bravo, Prof. Jones.
I am just an instructor.

Quote Quote by cabraham
There is no literal Coriolis force actively influencing the missile trajectory, but rather it is a correction term accounting for the deviation AS IF THERE WAS a "real" Coriolis force. The force is not literal, but the missile's path deviation is absolutely real. Coriolis force is a virtual force mathematically defined to account for A VERY REAL NON-FICTITIUOS path deviation.
Yes, As a student, I had to do this type of a problem on my third-year mechanics final exam. We had to determine whether a hunter killed a duck.

I, however, would not call a Coriolis force a correction term, it's a term that appears in rotating reference frames, just as centrifugal force does. The path of a particle is real, but the shape of the path is very dependent on the coordinate system used. Coriolis force and centrifugal account for the shape of the path in a rotating (with respect to an inertial frame) reference frame.

As D H and Doc Al (and possibly others) have said, it's crazy not do some problems in a rotating frame. When doing such problems, Coriolis force and centrifugal force are treated as real forces for which intuition developed doing more elementary Newton's second law problems can be used. But it should be kept in mind that these forces are just artifacts of a non-inertial coordinate system.

Consider accelerometers that consist of two main parts - a hollow sphere like a basketball inside of which is a slightly smaller sphere. Initially, the centres of the spheres coincide, so that there is a small, uniform gap between the spheres. During acceleration, the gap will be closed, and contact between the spheres will be made. An alarm that indicates acceleration motion will sound. For zero acceleration, no alarm will sound, and straight line motion in inertial frames is indicated.

An accelerometer won't measure acceleration due to either Coriolis force or to centrifugal force.

Also, if a freely falling accelerometer is small enough that tidal forces can be neglected, it will measure zero acceleration, since both spheres fall at the same rate. Acceleration due to gravity, just like acceleration due to Coriolis and centrifugal forces, is independent of mass. Can gravity, too, be considered to be an artifact of a coordinate system? No and yes.

Centrifugal and Coriolis forces at all points in space, i.e., globally, can be transformed away by a single transformation from the rotating frame to an inertial frame. For this reason, these forces are called fictitious. No single transformation will transform gravity away globally, but gravity can be transformed away locally by moving to a freely falling frame. If we expand the term "fictitious force" to include to forces that can be transformed away locally, then gravity also is a fictitious force. Pursuing this line of thought leads to the concept of gravity as spacetime geometry.

I repeated the points that D H and tiny-tim have made, using slightly different words.

As Doc Al has said, in mechanics courses, gravity is treated as a real force; it would be crazy to do otherwise. Considering gravity to be due to spacetime geometry, however, expresses something deeper about the physical world.
cabraham
#70
Jul2-08, 08:30 AM
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Quote Quote by George Jones View Post
I am just an instructor.



Yes, As a student, I had to do this type of a problem on my third-year mechanics final exam. We had to determine whether a hunter killed a duck.

I, however, would not call a Coriolis force a correction term, it's a term that appears in rotating reference frames, just as centrifugal force does. The path of a particle is real, but the shape of the path is very dependent on the coordinate system used. Coriolis force and centrifugal account for the shape of the path in a rotating (with respect to an inertial frame) reference frame.

As D H and Doc Al (and possibly others) have said, it's crazy not do some problems in a rotating frame. When doing such problems, Coriolis force and centrifugal force are treated as real forces for which intuition developed doing more elementary Newton's second law problems can be used. But it should be kept in mind that these forces are just artifacts of a non-inertial coordinate system.

Consider accelerometers that consist of two main parts - a hollow sphere like a basketball inside of which is a slightly smaller sphere. Initially, the centres of the spheres coincide, so that there is a small, uniform gap between the spheres. During acceleration, the gap will be closed, and contact between the spheres will be made. An alarm that indicates acceleration motion will sound. For zero acceleration, no alarm will sound, and straight line motion in inertial frames is indicated.

An accelerometer won't measure acceleration due to either Coriolis force or to centrifugal force.

Also, if a freely falling accelerometer is small enough that tidal forces can be neglected, it will measure zero acceleration, since both spheres fall at the same rate. Acceleration due to gravity, just like acceleration due to Coriolis and centrifugal forces, is independent of mass. Can gravity, too, be considered to be an artifact of a coordinate system? No and yes.

Centrifugal and Coriolis forces at all points in space, i.e., globally, can be transformed away by a single transformation from the rotating frame to an inertial frame. For this reason, these forces are called fictitious. No single transformation will transform gravity away globally, but gravity can be transformed away locally by moving to a freely falling frame. If we expand the term "fictitious force" to include to forces that can be transformed away locally, then gravity also is a fictitious force. Pursuing this line of thought leads to the concept of gravity as spacetime geometry.

I repeated the points that D H and tiny-tim have made, using slightly different words.

As Doc Al has said, in mechanics courses, gravity is treated as a real force; it would be crazy to do otherwise. Considering gravity to be due to spacetime geometry, however, expresses something deeper about the physical world.
Begging to differ, I don't quite follow you when you say Coriolis is not a correction term, but a term which "appears" in rotating ref frames. I guess different physicists, including the ones that taught me at my university, can view things differently. Call me a Newtonian curmudgeon if you please, but I don't see how an *accelerated" ref frame can be 1 to 1 "mapped" or "transformed" into a stationary one.

Let's take Coriolis. If we were to assume that the earth is NOT rotating, i.e. a stationary ref frame, while it actually IS rotating, what are the consequences? We err by not accounting for the rotation. So, we introduce a correction term in the kinetics/kinematics equations to account for this. But by doing so we are acknowledging the existence of rotation and an accelerated frame of ref. We say that we refer to earth as a frame of ref, but we do so with a priori knowledge that it is rotating. Thus we include the Coriolis term, twice the cross product of omega and u, to account for the rotation.

I guess one could look at it your way, that the Coriolis force is "there" in the rotating ref frame. When a projectile is launched near the equator, in a direction away from the equator, the rotation of the earth gives the missile a large eastward component of velocity. The eastward component of points on the earth further from the equator is less. I'm speaking of linear velocity, not rotational, i.e. u = r* omega. In flight, the missile moves north (or south) away from the equator, while maintaining its eastward velocity imparted via earth rotation. When the missile lands, it has outdistanced its *intended* landing spot wrt eastward velocity. Hence it lands east of the spot expected if earth rotation was neglected. I guess you could view it that way, but it can also be viewed as a correction term. With respect to the earth ref frame, a "virtual" force knocked the missile of course in the eastward direction.

The Coriolis term is intuitive and logical. There seems to be unanimous agreement that there is no actual "Coriolis force" knocking the missile eastward, i.e. Coriolis is "virtual". But in the course of the missile flight, where does "centrifugal" come into play? No one seems to produce the origin of this force, but are too quick to defend its significance. Also, no one has yet explained the origin of cf in the moon orbit question I raised earlier. Is anybody going to attampt to tackle that one? BR.

Claude
tiny-tim
#71
Jul2-08, 08:53 AM
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Quote Quote by cabraham View Post
The Coriolis term is intuitive and logical. There seems to be unanimous agreement that there is no actual "Coriolis force" knocking the missile eastward, i.e. Coriolis is "virtual". But in the course of the missile flight, where does "centrifugal" come into play? No one seems to produce the origin of this force, but are too quick to defend its significance.
Hi Claude!

Centrifugal force comes in as part of g.

It depends only on position, just like gravitational force, and so it's just part of what we measure as g (which isn't exactly "vertical" anyway, because of mountains etc).
Also, no one has yet explained the origin of cf in the moon orbit question I raised earlier. Is anybody going to attampt to tackle that one?
Which post was that?
Doc Al
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Jul2-08, 09:06 AM
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Quote Quote by cabraham View Post
Begging to differ, I don't quite follow you when you say Coriolis is not a correction term, but a term which "appears" in rotating ref frames. I guess different physicists, including the ones that taught me at my university, can view things differently. Call me a Newtonian curmudgeon if you please, but I don't see how an *accelerated" ref frame can be 1 to 1 "mapped" or "transformed" into a stationary one.

Let's take Coriolis. If we were to assume that the earth is NOT rotating, i.e. a stationary ref frame, while it actually IS rotating, what are the consequences? We err by not accounting for the rotation. So, we introduce a correction term in the kinetics/kinematics equations to account for this. But by doing so we are acknowledging the existence of rotation and an accelerated frame of ref. We say that we refer to earth as a frame of ref, but we do so with a priori knowledge that it is rotating. Thus we include the Coriolis term, twice the cross product of omega and u, to account for the rotation.
I suppose you can consider analyzing motion that takes into account the earth's rotation as a "correction" to an analysis that ignores the earth's rotation. But that's not what is being discussed here. We are talking about analyzing things from an inertial, non-rotating frame (in which the earth rotates, of course!) versus analyzing things from a non-inertial, rotating frame (in which the earth is at rest). We are not talking about ignoring the earth's rotation versus taking it into account. (Both frames take rotation into account!)

When we say that coriolis and centrifugal forces are artifacts of using a non-inertial, rotating frame that does not mean that new physical effects magically appear when using a rotating frame of reference. The physical effects exist even in an inertial frame--they are just much harder to analyze! (In an inertial frame, the effects are "simply" due to the fact that while a projectile goes "straight", the earth rotates.) If you do your analysis from an inertial frame, there is no need to introduce "forces" such as centrifugal or coriolis. (But good luck carrying out that analysis!)

Also, no one has yet explained the origin of cf in the moon orbit question I raised earlier. Is anybody going to attampt to tackle that one?
I thought I answered that in post #51.


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