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Foucault Pendulum

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Published on Feb 5, 2008

This is a video compilation of a Foucault pendulum in action at the Houston Museum of Natural Science. The rotation of the plane of the pendulum's oscillations demonstrates that the earth is a rotating reference frame. The number of rotations it makes in one day (about 180 degrees in 24 hours) also indicates the latitude of the museum (about 30 degrees north of the equator).

By my count, there must be exactly 144 pins forming a circle on the floor underneath the pendulum. In the video, you will see two pins get knocked over, 1 hour apart. There was another pin between these two that gets tipped over, but this event is not on the video.

With this data, I expect the time for two adjacent pins to get knocked over to be 48/144 = 0.33 hours. Between the 3 pins getting knocked over, it should have taken only 40 minutes, not 1 hour. Perhaps the spacing or position of the pins were uneven?

At latitude L in the northern hemisphere, the plane of the pendulum's oscillations rotates clockwise by the amount 360*sin(L) degrees in one day. One can google to find out how this expression can be obtained, but let me point out two illuminating remarks regarding this expression: (1) It is the projection of the angular velocity of the earth (magnitude 360 degrees per day) onto the vertical direction at latitude L. (2) It is related to the net rotation of a vector resulting from parallel transport along a closed circuit on the surface of a sphere. This rotation is given by the solid angle subtended by the surface enclosed by the circuit. In the case of our pendulum, the circuit is the circle of latitude. We get 360*sin(L) after subtracting 360 from the solid angle subtended by the surface enclosed by the circle of latitude and that includes the north pole.

The museum is at latitude 29 deg 46 min N, according to the touch-screen panel near the pendulum. My old Magellan handheld GPS reported coordinates of 29 deg 43.281 N, 95 deg 23.353 W, 23 ft, which is pretty close. Plugging L~30 deg into our formula, we get 360*sin(30)=180 deg/day.

Other facts I learned from the touch-screen:
Pendulum weight - 180 lbs (81.6 kg)
Length - 61.6 feet (18.8 m)
Period - 8.71 sec
Swing angle - 5 deg
Displacement - 65 inches (1.65m)

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