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# Coriolis Force

## Discussion

Should this be changed to a discussion of radial vs. tangential acceleration?

Pendulum

Quotes that need to be paraphrased

• Understanding the motion of such a pendulum at Earth's North Pole is simple and intuitive: the plane of oscillation remains fixed relative to the distant stars while Earth rotates underneath it at a rate of 360° per day. The situation is much more difficult to visualize for locations away from the pole. For a pendulum at latitude λ, the plane of oscillation rotates at the slower rate of 360° × sin λ per day. The rate of rotation becomes zero at Earth's equator (λ = 0), and the rotation reverses direction in the Southern Hemisphere. A rigorous derivation of the "sine law" fills several pages with vector cal- culations in advanced undergraduate mechanics textbooks, which use the pendulum as an example of how the Coriolis force acts on a moving object in the noninertial frame of the rotating Earth. Foucault's experimental results matched the prediction of the sine law and his demonstrations cap- tured the imagination of the general public. The day that appears in the sine law is the sidereal day of about 23 hours 56 minutes, which is the time for the Earth to rotate once relative to the frame of the distant stars.

Quote that needs to be verified

• Léon Foucault, Recueil des travaux scien- tifiques de Léon Foucault (Gauthier-Villars, Paris, 1878), p. 378. This 1878 collection quotes Foucault's handwritten note, which can be trans- lated as: "Wednesday, January 8, at 2:00 a.m.: the pendulum turned in the direction of the diurnal motion of the celestial sphere." The date of the first successful observation is sometimes given incorrectly as 2:00 a.m. on January 6, 1851 (see Ref. 8, p. 5). But in 1851, January 6 was a Monday, while January 8 (the correct date) was a Wednesday.
Acceleration in a rotating coordinate system
direction real fictitious