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    Re: Coriolis and gyros (second attempt)(typos corrected)
    From: Peter Hakel
    Date: 2009 Aug 25, 15:58 -0700
    Inertial reference frames are indeed intuitively "better" than non-inertial ones because they don't use these "fictitious" forces.  This view predates Einstein, who has shown that non-inertial frames are no worse - since an inertial frame with gravity is equivalent to a non-inertial frame without gravity.  BTW, by your reasoning magnetic fields and forces are also fictitious because they only appear in reference frames that see electrical currents, i.e. in those that are not co-moving with the charges.

    I am not telling you that your "inertial" point of view is wrong.  I simply defend the place that non-inertial frames have in our current understanding of how the world works.  They are not fiction that we invent for computational convenience.

    This is all rather non-intuitive but such is much of 20th century physics.  You may compare it to storks and fairy tales, but that doesn't change the fact that this physics works very well, for example in GPS.

    I don't think we are getting anywhere with this debate.  As I said before, in some sense we are both right (after all, it's about relativity!  :-) ) so let's just leave it at that, fair enough?

    Peter Hakel

    From: Gary LaPook <glapook---.net>
    To: navlist@fer3.com
    Sent: Tuesday, August 25, 2009 1:59:22 AM
    Subject: [NavList 9621] Re: Coriolis and gyros (second attempt)(typos corrected)

    Note, I am not saying that the use of a "fiction" might not be useful in
    making an explanation for what an observer is seeing just like you
    telling your young child that the stork brought the new baby.


    Gary LaPook wrote:
    > It's still just a "fictitious" force used to explain to an observer on
    > earth what he thinks he is seeing. Think about this one. Say you are
    > in a space ship in the coasting phase of an interstellar mission
    > moving at a constant velocity, not accelerating or rotating, not
    > subject to any real forces--an inertial reference frame. You have a
    > gyroscope on board and you point one end of its axis of rotation at
    > Sirius. Due to the gyroscopic property of "rigidity in space" it will
    > stay pointed at Sirius. Now do the same experiment on our rotating
    > earth.  Point the axis of a gyroscope at Sirius and it will continue
    > to point at Sirius due to the same "rigidity in space" while the earth
    > turns under it. No need for a force to keep it pointed at Sirius in
    > the space ship and no need for a force to keep it pointing at Sirius
    > on earth either.
    > gl
    > P H wrote:
    >> Gary,
    >> First, let's agree that the pendulum has a "small" amplitude (say
    >> within 5 degrees), so that the idealized pendulum model is adequate. 
    >> Then its natural oscillations have a single frequency which is
    >> independent of the amplitude.  The maximum amplitude, velocity, and
    >> acceleration of the bob are all directly proportional to one
    >> another.  So, when you double the amplitude scale (within those 5
    >> degrees...), you also double the velocity scale.
    >> Now add a small perturbation in the form of Earth's rotation
    >> underneath the pendulum.  As you correctly point out, the Coriolis
    >> force/acceleration is linearly proportional to velocity.  This small
    >> correction has to be added to the unperturbed velocity.  The outcome
    >> of this addition is the Foucault rotation.  Both the unperturbed
    >> velocity and the Coriolis correction to it will scale together in
    >> magnitude, hence halving one will halve the other.  The resulting
    >> rotation angles are therefore independent of the pendulum's amplitude
    >> and its velocity.  Since the oscillation time scale is unaffected by
    >> amplitude, you get the independence of the Foucault rotation rate as
    >> well.  Everything checks out.
    >> We can also recall that the mass of the bob plays no role in this
    >> analysis.  This is consistent with the notion that gravitational and
    >> inertial accelerations (such as Coriolis) are independent of the mass
    >> -  as they should be, since they are in fact equivalent.
    >> Peter Hakel
    >> ------------------------------------------------------------------------
    >> *From:* Gary LaPook <glapook---.net>
    >> *To:* navlist@fer3.com
    >> *Sent:* Monday, August 24, 2009 10:29:08 AM
    >> *Subject:* [NavList 9614] Re: Coriolis and gyros (second
    >> attempt)(typos corrected)
    >> There is a problem with your analysis.
    >> Since the period of the pendulum is fixed by its length then it is
    >> necessarily true that as the amplitude of the swing diminishes during
    >> the day, due to air resistance, that its maximum velocity and its
    >> average velocity also slows down. Try this yourself with any pendulum
    >> and observe how slowly it moves near the end as it slows to a stop. The
    >> formula for coriolis force includes a term for velocity across the
    >> turning reference frame so that coriolis force and coriolis acceleration
    >> is proportional to this velocity over the ground. So if your analysis is
    >> correct then the rate of change of the azimuth of the pendulum's swing
    >> should vary throughout the day, changing at a more rapid rate in the
    >> morning and more slowly later in the day as the pendulum slows down. But
    >> the rate of change of azimuth is constant, 11.32 degrees per hour which
    >> disproves your analysis.
    >> Now looking at the case of the gyroscope's undergoing earth rate
    >> apparent precession. If this apparent precession  is caused by coriolis
    >> due to the speed of the rotating flywheel moving in one direction at the
    >> point at the bottom and in the opposite direction at the top, (as you
    >> claim) then, without doing the diagram of the precessional forces (I
    >> leave that to you), it must also be true that gyroscopes spinning in
    >> opposite directions would also precess in opposite directions. One
    >> rotating clockwise would precess toward the east and one turning
    >> counterclockwise would precess toward the west yet all gyroscopes, no
    >> matter which way they are spinning, precess toward the east, again
    >> disproving your analysis.
    >> A further disproof of your analysis of earth rate precession of a
    >> gyroscope is due to that pesky term in the coriolis formula that makes
    >> the coriolis force proportional to velocity over the ground. If your
    >> analysis were correct then slowly turning gyroscopes would precess more
    >> slowly than rapidly spinning gyros yet they all show the same apparent
    >> precession due to the earth rate of 15.04 degrees per hour times the
    >> sine of the latitude.
    >> You have not addressed the movement of a gyrocompass at the equator
    >> where coriolis is zero since the sine of zero degrees of latitude is
    >> also zero, there's that pesky coriolis formula again.
    >> Also consider the earth rate apparent precession of a gyroscope at the
    >> north pole which changes at a rate of 15.04 degrees per hour since the
    >> sine of 90 degrees of latitude is 1. Yet a gyroscope located exactly at
    >> the pole is not moving at all (ignoring the earth's movement around its
    >> orbit) but is remaining at one fixed spot on the earth so it has no
    >> velocity across the ground so, again by the formula, there should be no
    >> coriolis available to cause the apparent precession.
    >> gl
    >> frankreed{at}HistoricalAtlas.com <mailto:frankreed{at}HistoricalAtlas.com>
    >> wrote:
    >> > "Coriolis is not involved since the Pantheon has not moved across
    >> the surface of the earth since its foundations were laid in 1758 so
    >> its ground speed is zero."
    >> >
    >> > LOL. Gary the pendulum bob is itself in motion, right? Its ground
    >> speed is most certainly NOT zero. Likewise in a gyro-compass, its
    >> individuaL mass elements are moving at very high speed. If they
    >> weren't moving, it wouldn't work. The Coriolis acceleration causes
    >> the precession in both cases --in the rotating frame of reference in
    >> which the Earth is fixed.
    >> >
    >> > -FER
    >> >
    >> >
    >> >
    >> > >
    >> >
    >> >
    > >

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