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 26 April 2024 23:17

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Question
Asked by: Harvey Fiala
Subject: Simple Gyroscopic Precession
Question: TAKE HOME QUIZ # 3: Gyroscopic Precession
Assume the earth were a hollow spherical shell with the thickness of the spherical shell equal to only one foot and the outer diameter of the shell were exactly equal to that of the earth. Assume the density of the shell was uniform and great enough so that the gravitational force at the surface of the shell was exactly equal to the gravitational force (g) at the surface of the real earth. Then from all external appearances, the real earth and the hollow shell would look alive and have identical external gravitational fields.

1. How does the gravitational field strength vary from the outside surface of the one-foot thick shell to its inner surface? Assume the gravitational field strength at the surface of the earth is simply g (32.2 ft/sec2).

2. Calculate the gravitational field strength inside the hollow shell as a function of the radial distance from the center.

3. Assume the earth is the hollow spherical shell described above. Assume that a gyro were undergoing natural precession due to the gravitational field on a pivot point just above the surface of the earth. Let the precessional angular velocity be ωp . Now assume the same gyro were on a pivot point only one foot lower, just at the inside surface of the spherical shell. With everything else being equal except the gyro is now at the inner surface of the shell instead of on the outer surface of the shell, what is the new precessional angular velocity due to natural precession?
Date: 27 October 2004
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