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Re: non-inertial frames



As an example of the deleterious effects of too much meditation on
centrifugal forces, consider the following little essay on tides from
an introductory oceanography text (An Introduction to the World's
Oceans, Duxbury and Duxbury).

"The Moon orbits the Earth, held by the Earth's gravitational force
acting on the Moon (B). There is also a force acting to pull the Moon
away from the Earth and send it spinning out into space (B'); [Note
that the source of this force is left unidentified.] this is
considered a centrifugal force in our discussion. Forces B and B'
must be equal and opposite to keep the Moon in its orbit. Likewise
the Moon's gravitational force acting on the Earth (C) must be
balanced by the centrifugal force (C'). B' and C' are caused by the
Earth-Moon system rotating about an axis at the center of the
system's mass . . . The Earth-Moon system is held in orbit about the
Sun by the Sun's gravitational attraction (A). A centrifugal force
again acts to pull the Earth-Moon system away from the Sun (A'). To
remain in this orbit, the Earth-Moon system requires that the
gravitational forces equal the centrifugal forces."

There follows a brief description of the inverse square law for
gravity.

"If the distribution of gravitational and centrifugal forces is
calculated for each gram of material at the Earth's surface and also
at its center, the forces at the Earth's surface are found to be
different from those at its center because of the change in value of
the distance between a particle and the tide-raising body and also
because of the distance between a particle and the Earth-Moon
system's axis of rotation. The Earth-Moon-Sun system is in balance at
the Earth's center (gravitational forces balanced by centrifugal
forces), but these forces are not in balance between points on the
Earth's surface."

"The water particles on the side of the Earth facing the Moon are
closest to the Moon and are acted on by a larger Moon gravitational
force than is present at the Earth's center. Because the water
covering is liquid and deformable, this force moves the water
particles toward a point directly under the Moon. This movement
produces a bulge in the water covering. At the same time, the
centrifugal force of the Earth-Moon system acting on the water
particles at the Earth's surface opposite the Moon is larger than
that present at the Earth's center, creating a bulge."

There is a nice accompanying figure illustrating how the
gravitational force dominates the centrifugal on one side of the
Earth and how the centrifugal dominates the gravitational on the
other side.

Forces are interactions between objects and necessarily come in
pairs. If you can't identify the other object (and you can't with a
centrifugal "force") then it ain't there. It is an effect, not a
force.

Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29526 variety in unity.
pjcamp@csd1.coastal.edu --Umberto Eco
(803)349-2227 The Name of the Rose
fax: (803)349-2926