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Re: [Phys-l] NYT article: Centrifugal force



An addendum to my previous post:

An interesting article by Mahazzabi and James [AJP, 68, 1038, (November 2000)] shows that the standard textbook calculation is wrong, specifically, that it is low by a factor of two as a result of the fact that the flattening itself causes the Newtonian contribution to g to deviate in the same direction by the same amount as the centrifugal contribution. The article also has a concluding paragraph that is relevant to this discussion:

In addition to giving the correct equation for plumb line deviation, we have shown how the elliptic shape of the earth, as well as its degree of ellipticity, can easily be obtained from this equation with a very high degree of accuracy, all at a level comfortably accessible to introductory physics students. Furthermore, we have treated the problem in an inertial coordinate system without introducing the fictitious centrifugal force. Although physics in noninertial reference frames is well developed and quite sound, introductory students are often quite reluctant to discard their erroneous belief in a real centrifugal force which pulls outward on a rotating body. Indeed, it was only when Hooke taught Newton to analyze circular motion in terms of a centripetal acceleration, discarding the notion of a real centrifugal force, that Newton was able to compose his law of universal gravitation which consolidated the celestial motions with terrestrial observations of gravity and the shape of the earth.


John Mallinckrodt
Cal Poly Pomona

I wrote:

On Jul 3, 2009, at 6:43 AM, alex brown wrote:

How would one go about calculating this one third of a degree?... I
would just like to know the starting point so I can have a go. Thanks

This used to be a fairly standard problem in introductory textbooks.
Usually it was presented in terms of finding the deviation of a plumb
line from the direction to the center of the Earth. The analysis was
generally done in an inertial frame so the question amounts to what
is the tension (magnitude and direction) such that, when added to the
(Newtonian) gravitational force, the net force provides the proper
centripetal acceleration for the plumb bob. At mid latitudes the
angular deviation is about a tenth of a degree, not a third of a
degree, or 20% of the angle subtended by the moon.