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    Re: Air Hockey Pucks and Gravity
    From: Lu Abel
    Date: 2008 Feb 01, 09:31 -0800

    frankreed@HistoricalAtlas.net wrote:
    > **Above I mentioned the tidal period. So there's no confusion, I'm not
    > talking about ocean tides due to the variation in the gravitational forces
    > of the Sun and the Moon over the surface of the Earth, but rather the local
    > "tidal" acceleration in the vicinity of any point on Earth due to the
    > variation in the gravitational force of the Earth itself. For an example,
    > imagine an air table with a disc on it ("air hockey" with a floating puck).
    > If I level the table perfectly at its center, and if the table is perfectly
    > flat, then the floating disc, if released near one edge, will "fall" towards
    > the center because that's the only place where the gravity vector is exactly
    > perpendicular to the table --everywhere else, the vector is slightly tilted,
    > pointing towards the center of the Earth, so a small component of the
    > gravity vector is pointing towards the center of the table. The amount is
    > directly proportional to the distance from the center of the table. The disc
    > will execute simple harmonic motion [natural frequency
    > omega=sqrt(g/R)=sqrt(GM/R^3)], as if it's attached to the center of the
    > table by a perfect spring, gliding back and forth across the table with a
    > period of 84 minutes (ignoring air resistance). Give it a slight sideways
    > motion and the disc will travel in a circular or elliptical path around the
    > center of the table with that same 84 minute period (no matter how big the
    > circle). That's the "tidal field" of the Earth.
    >
    I challenged several of my smart friends with this problem.   After they
    found the solution, one of them asked if the axis of the puck's
    back-and-forth motion will rotate because it is in fact a Foucault
    pendulum.   I suspect it would.   But another asked about Coriolis
    forces on the back-and-forth motion and I didn't have an answer.   Would
    the Coriolis force just be another manifestation of the Foucault effect?
    
    Lu Abel
    
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