--- On Thu, 7/2/09, Anthony Lapinski <Anthony_Lapinski@pds.org> wrote:
"I always thought that the Earth bulges due to inertia, not forces.
Particles on the equator naturally want to go on a tangent."
True for an INERTIAL observer not participating in the Earth's rotation.
However, for us, sitting on Earth, there is no going on a tangent because there are no parts in relative motion with respect to each other. For us, the bulging in the Earth's RF is caused by centrifugal force. The same holds for a merry-go-round, when the chairs are deflected radially away from the rotational axis. In the language of GR, it is just an additional component of gravity force emerging in any accelerating RF.
The negative attitude to the centrifugal force is caused by an unfortunate use of the term "fictitious force" as an absolute concept applicable in ALL RF, which is totally wrong.
" I tell my students that every force must have a source!"
Correct again, but only if we caution them that this is generally not true in an accelerating RF. In the latter there appears additional gravity field independent of the source. Moreover, it may exist even without any physical source (as an e.g., consider teaching the students in the same merry-go-round or in a spinning space-station for that matter, with negligible mass, in a free space). The undeniable force there is the centrifugal force in the HS language, and the gravity force in the GR language, it is two different names for the same thing. The difference between the gravity having a source and the RF-induced gravity is that the latter, first, does not go to zero at infinity, and second, can be eliminated by an appropriate change of RF. IN other words, the second component of gravity, while being as real as one can get, does not cause the space-time distortion.
"When you go on the "Gravitron" (rotor) ride at the amusement park, you do
feel an outward force. It's simply the reaction force (you on wall) to the
centripetal force (wall on you). It's called a centrifugal force but it
acts on the wall, not you. Thus, it's not part of the free-body diagram
(on you)."
Again, this explanation holds in an inertial RF, but not in yours one. If there is no other force on you except for the centripetal force from the wall, then you should accelerate toward the center. Such acceleration is indeed, recorded by an external observer from an inertial RF, but is not observed by you when plastered against the Gravitron's wall. You do not have any velocity relative to the center and do not accelerate toward it. It is because the normal force on you from the wall is exactly balanced by the centrifugal (gravitational - choose according to your taste) force on you there.