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    Re: Coriolis and gyros (second attempt)(typos corrected)
    From: Gary LaPook
    Date: 2009 Aug 25, 16:42 -0700

    It's been an interesting discussions and I will take your suggestion.
    On Aug 26, 12:58�am, P H  wrote:
    > 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 
    > 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.
    > gl
    > 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 
    > >> *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
    > >> frankr...@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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