# Talk:Centrifugal force (rotating reference frame)

Active discussions

## Not to be confused with

There are various warnings not to confuse various forces: Centrifugal force, Reactive centrifugal force, Centripetal force, Centrifugal force (rotating reference frame). There is however no discussion of the distinction between these various phenomenon. --Kvng (talk) 20:46, 2 July 2012 (UTC)

## More properly an effect than a force?

I suspect that the lead would be better if reworked à la N.M.J. Woodhouse, who writes (p. 7) in his Special Relativity (Springer-Verlag, 2003),

"In problems where the rotation matters, for example in the analysis of Foucault's pendulum, it is helpful to treat a terrestrial frame as if it were intertial, but to introduce correction terms, the 'fictitious' centrifugal and Coriolis forces, to take account of the rotation. But these are not real forces, and the frame is not really inertial."

Indeed, even Wikipedia's own article on Coriolis forces is a redirect to Coriolus effect, and that article makes it clearer than this one does that the force is only apparent. I'd have just changed it myself, but wondered if there were a good argument for retaining the nonparallelism of treating one of the two forces as though it were somehow less fictitious than the other.—PaulTanenbaum (talk) 20:57, 19 February 2013 (UTC)

My two cents here - I think there is a distinction between "effect" and "force" in these instances. My feeling from the literature that I've read is that the effect refers to the apparently anomalous deflection of the path of a particle while the force is the pseudo-force or fictitious force that is introduced to explain the deflection. As for an argument for retaining the nonparallelism, this is what we find in the literature, ie the terms "Coriolis effect" and "Coriolis force" are used with about the same frequency and sometimes it seems inter-changeably. The choice also seems to be dependent on the context - in meteorology we find "Coriolis effect" (and my guess this is true for the everyday person), while in the physics literature "Coriolis force" is more common. I don't think the same can be said for "centrifugal force"/"centrifugal effect". Just to get a general idea of how common the terms occur in the literature I searched for each phrase in google books:
• Coriolis effect : ~44,500
• Coriolis force : ~138,000
• Centrifugal effect : ~16,700
• Centrifugal force : ~1,260,000
That's almost two orders of magnitude difference for centrifugal between effect and force, while for Coriolis the two are roughly equal (okay, a factor of about 3 but less than an order of magnitude). So imo I don't care whether the other article is "Coriolis effect" or "Coriolis force", but I strongly favor keeping this one as "centrifugal force" per the usage frequency in the literature. That being said, if the intro needs to be clearer on it being a fictitious force then that should be fixed. --FyzixFighter (talk) 05:33, 20 February 2013 (UTC)
I agree with FF. If you want it more parallel, go the other way. And I'd avoid the notion of "only apparent", since we already have a well-define notion of "fictitious force" that says exactly what it is. Dicklyon (talk) 05:49, 20 February 2013 (UTC)

## Acceleration Derivation

In the derivation section, I'm noticing that the last two lines of equations in the "acceleration" section do not seem to follow from one another. When I evaluate the d/dt([dr/dt]+w x r) term in the next to last line, it does not give the factor of two in front of the Coriolis term. I believe the error is leaving out part of the first derivative operator: that is, in that equation, instead of the operator "d/dt" we should have "d/dt + w x" as the operator. (also see the rotational reference frame wiki page for that derivation, in which the derivation correctly gets the factor of two into the Coriolis term) I would just go ahead and add it, except I'm not at all familiar with the proper coding for inserting equations into wikipedia, and am very new here in general — Preceding unsigned comment added by 222.221.253.76 (talk) 02:13, 6 March 2013 (UTC)

It is correct. Don't forget that
${\displaystyle {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}=\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ ,}$
and of course likewise
${\displaystyle {\frac {\operatorname {d} }{\operatorname {d} t}}\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]\ ,}$
so that is where the second term comes from.
Note - this derivation could need a source. - DVdm (talk) 12:47, 6 March 2013 (UTC)

## It's the rotation of the direction of the velocity vector that matters, not of the frame.

Yep. We have here a misleading article title, and misleading wording that implies that a reference frame's rotation results in centrifugal force/pseudoforce. Rather, it's the centripetal acceleration of the frame (or object) that results in such forces. The centripetal acceleration of the frame (stated in an inertial frame) is proportional to the rate of change of the direction of the velocity vector (also stated in the same inertial frame). Thus, if the rate of rotation of anything matters, it's the rate of rotation of the direction of the velocity vector, not the rotation rate of the frame.

I grant that, in most usual cases (such as ball-on-string), the most common frame is attached to the object (ball) and is also rotating along with the object. The rotation rate of the frame in these cases is the same as the rotation rate of the direction of the velocity vector, but that's only incidental. It's the rate of change of the direction of the velocity vector that makes for the centrifugal forces here. If the frame was still attached to the ball, but was chosen to rotate at twice or three times the rate of the velocity vector, or if it was chosen to not rotate at all, it would not effect the magnitude of the centrifugal force, nor would it effect the actual direction of the centrifugal force. Such an independently-rotating frame would have different numbers representing the direction of the centrifugal force, but the actual direction (or magnitude) of the centrifugal force at any particular moment would not vary with rotation rate of the frame.

We should not muddle-together the movement of a frame (such as in a circle about a point) with rotation of the frame. They are two different things that can be independent. If we don't keep that in mind, it leads to fallacies.

Montyv (talk) 17:32, 31 May 2015 (UTC)