Underground Rivers - University of New Mexico

Case 1: Gravitation alone
Case 3: Gravitation plus 17.1 rotation/day
centrifugal force
Case 2 adds centrifugal force
Centrifugal force = m r ω 2
Chapter 14 -- Hollow Earth Geophysics
DRAFT 1122//66//22001122
Case 2: Gravitation plus 1 rotation/day
centrifugal force
Case 4: 17.1 rotation/day centrifugal force
alone
where r is the radius of rotation, 6371 kilometers for an object at the earth's equator, and
ω (omega) is the angular velocity, 1/day for the earth.
Centrifugal force is directed perpendicularly-outward from the axis. It is greatest at the equator
and zero at the poles, because there, r is zero.
Other rotations about axes in different orientations and of differing angular velocities could be
added -- spinning the spin, so to speak -- but regardless of how many spins are imposed, the
sphere ends up rotating about but one resultant axis at some constant ω. It's just a tipped
version of the same diagram with proportionally longer or shorter lines sideways to the axis.
We on earth are influenced by both gravitational and centrifugal force, but at a ω of 1
rotation/day, the centrifugal force on an object at the earth's surface varies from 1/300 of
gravitational force at the equator to zero at the poles. (We've exaggerated the illustrated
horizontal lines to make them apparent; plotted to scale, the longest of them would be but a linewidth
in length.) Thanks to the earth's spin, we weigh 3/10 of one percent less at the North Pole
than we do at the equator, but we don't find it worth hauling our scales to the Arctic.
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