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Re: Re; centrifugal force, was Banked road



At 10:26 PM 11/6/01 -0500, Ludwik Kowalski wrote:

The centrifugal force, fictitious to me but very real in the
rotating frame, would act on the bead ... as it
slides away from the axis of rotation.

Yes.

It is the only force acting on
the bead, like gravity in free fall.

Yes, it is like gravity, but it is _not_ the only force. There is also the
Coriolis contribution.

The object is experiencing "artificial
gravity" directed away from the axis of rotation.

But why should the same be true for somebody who is not in contact
with the rigid structure of the rotating pipe?

Contact has nothing to do with it. The observer's choice of reference
frame is what matters. According to an observer in the rotating reference
frame, every object obeys the law
F = m (x dot dot) (1a)
+ 2m omega (x dot) (1b)
+ m omega^2 x (1c)

which reduces to F=ma in the special case of omega=0.

An object half way between
the axis and the wall will not experience any radial pull toward the
nearest wall.

Huh? In the rotating frame, everything, absolutely everything, experiences
a radial pull due to centrifugal force, according to term (1c) in equation
(1) above.

Is it correct to say that artificial gravity exists only for
objects which are forced to rotate together with the pipe (like in a
centrifuge), it does not exist for all objects inside a rotating empty pipe?

I wouldn't say that. Emptiness has nothing to do with it. The observer's
choice of reference frame is what matters.

In the special case of an object that happens to be stationary in the lab
frame, it goes around in a circle in the rotating frame. According to the
rotating observer, the object does not accelerate outwards because the
centrifugal force is overcome by the Coriolis force. Indeed the object is
constantly accelerating inwards as it goes around the circle. At the speed
in question, the Coriolis force is twice as large as the centrifugal force,
so everything works out just right.