Centrifugal Force

[Charles Volk]

Dear Cecil,

In your recent column about the relationship between aging and latitude on the Earth you used the term "centrifugal force" when explaining why the earth bulges at the equator.

Centrifugal force is an imaginary force that describes the feeling one would experience in an accelerating reference frame. As the magnitude of the acceleration of the earth is relatively constant the term centrifugal force does not apply. I believe that centripetal acceleration (center seeking force) best describes the phenomenon you wish to convey.

Sincerely,

Charles Volk - San Luis Obispo, CA

[bibliophage]

Welcome to the SDMB, Charles.

A link to the column is appreciated. Providing one can be as simple as pasting the URL into your post, making sure to leave a blan space on either side of it. Like so: http://www.straightdope.com/classics/a4_183.html

Although centrifugal force is often called a "fictitious force," it's my understanding that under General Relativity, there's no meaningful distinction between "real" and "fictitious" forces in rotating reference frames, and no reason to prefer non-rotating over rotating reference frames. But I stand ready to take that back if corrected by somebody who knows more about it than I do.

[Cervaise]

How do you like my centrifuge, Mister Bond?

[Stranger On A Train]

Originally Posted by bibliophage

Although centrifugal force is often called a "fictitious force," it's my understanding that under General Relativity, there's no meaningful distinction between "real" and "fictitious" forces in rotating reference frames, and no reason to prefer non-rotating over rotating reference frames. But I stand ready to take that back if corrected by somebody who knows more about it than I do.

Slight correction; GR says that there are no differences between non-inertial (so-called "real") forces in an inertial reference frame (i.e. a reference frame that is not accelerating) and inertial (so-called "ficticious") forces in a non-inertial (accelerating) reference frame. From a very generalized standpoint there is always a force being applied somewhere in a system undergoing non-inertial motion; whether it is "real" or "ficticious" (i.e. arrising from a change in velocity) really just depends on where you are standing. For Mr. Bond, strapped inside the centerfuge, the outward force pulling him down and crushing him against the ring is very much real and measurable, and indeed, by itself indiscernable from a non-inertial force like gravity.

However, unlike a system undergoing linear acceleration (say, a rocket thrusting in a straight line) which is, for the subject, completely indistinguishable from acceleration due to gravity, the characteristics of a rotating system can be determined within the system by measuring the Coriolis component, which arises from the appearance of acceleration by an object whose motion is not aligned with the rotating coordinate frame. This is what causes the self-correcting motion of a gyroscope (motion off-axis results in a counter force that tends to return it to original orientation, albeit resulting in an oscolation) and causes winds to curl off the equator and move toward the poles. So rotating systems are "special" and identifible in that sense, and can be identified even using very primitive equipment like Foucault's Pendulum (the oscillating apparatus, not the Umberto Eco novel, for which no functional use has yet been determined.) Objects under variable rotation also experience another component called the Euler force. Again, this arrises from a change in inertia of the rotating system, and so externally is an abstraction created by the couple between the external force causing variation and either the system's overall inertia (for an ungrounded system) or the axle about which the system rotates.

It may seem odd that one part of the system can be under acceleration even though no external force is applied, until you realize that (for a balanced rotating system) an equal and opposite acceleration is occuring on the other side of the system. When you sum up all the components you find that although there is a "felt" force at any given point off the axis of rotation, the net force on the overall system is still zero, hence why crackpot attempts to make reactionless rockets using gyroscopes never works. Of course, if that force results in a change in the mass properties of the system (say, you suddenly shift a bunch of mass from one side of your rotating space station to another) then you'll get an imbalance that will cause the axis of rotation to shift to the center of mass, and you'll get nutational oscolations (slight in-plane wobbling). If you stick mass up out of the plane of rotation, you'll get a couple that causes precession.

Centripetal force--the "center-seeking force" to which the o.p. refers--is a force required to keep an object rotating in a circle (or ellipse or indeed any parabolic path, but we'll stick with circles for now). Centripetal force isn't really a specific type of force; it's just a stand-in for some other "righting" force; say, the tangental rigidity of a wheel, the tensile force of a string, or the attractive acceleration of gravity around a large mass. For the Earth, the centripetal force is the latter; gravity holds the mass of the Earth in a rough sphere (the tensile strength of the crust is essentially nil), and centrifugal force arrising from the rapid spinning motion of the Earth causes it to be an oblate spheroid.

Stranger

[Chronos]

Centripetal force--the "center-seeking force" to which the o.p. refers--is a force required to keep an object rotating in a circle (or ellipse or indeed any parabolic path, but we'll stick with circles for now). Centripetal force isn't really a specific type of force; it's just a stand-in for some other "righting" force; say, the tangental rigidity of a wheel, the tensile force of a string, or the attractive acceleration of gravity around a large mass. For the Earth, the centripetal force is the latter; gravity holds the mass of the Earth in a rough sphere (the tensile strength of the crust is essentially nil), and centrifugal force arrising from the rapid spinning motion of the Earth causes it to be an oblate spheroid.

To put it another way, a force is classified as centripetal force by virtue of what it does (causing something to move in a curved path rather than a straight line), whereas a centrifugal force is classified by how it arises (from the bookkeeping involved in a non-inertial coodinate system).

The formulas for centrifugal force and centripetal force look the same, but they're actually completely separate forces, and don't even exist in the same coordinate system. If you're working in the co-rotating coordinate system (which is convenient if, for instance, you want your coordinate system to be attached to the Earth), then you have a centrifugal force, but no centripetal force. If, however, you're working in an inertial coordinate system, then one of the forces in your system is a centripetal force, but there is no centrifugal force. So long as you're consistent about which system you're working in, neither is incorrect.

[DSYoungEsq]

Originally Posted by Cervaise

How do you like my centrifuge, Mister Bond?

Priceless!!!!


That site just got added to my favs, right quick!!

[SiXSwordS]

Originally Posted by Stranger On A Train

...[R]otating systems are "special" and identifiable in that sense, and can be identified even using very primitive equipment like Foucault's Pendulum (the oscillating apparatus, not the Umberto Eco novel, for which no functional use has yet been determined.)

emphasis mine

My level of offense taken at that wholly uncalled for slur is not sufficient for a pitting. Is it proper to Cafe Society someone?

As usual, Stranger your grasp of the concepts in question is impressive and your willingness to share is worth a few bucks all by itself.

[Stranger On A Train]

Originally Posted by SiXSwordS

My level of offense taken at that wholly uncalled for slur is not sufficient for a pitting. Is it proper to Cafe Society someone?

Actually, I rather like Eco, but I'll be damned if I can make heads or tails of Foucault's Pendulum. It's one of those books I have on the list to sit down and read in its entirety with the collection of references on hand to cross against, but not any time soon. Mostly the comment was just a chance to make a cheap joke at Uncle Umberto's expense.

Stranger

[SiXSwordS]

I think the key to the novel is really in the section about Belbo's youth in Italy. You're right, though, it is a bit opaque.
end of hijack

[Cervaise]

A bit!?

(And I'm a huge fan of the book.)