"Dan Bloomquist" <public21@[EMAIL PROTECTED]
> wrote in message
news:z4IAj.5779$7d1.1603@[EMAIL PROTECTED]
> daestrom wrote:
>>
>>
>> But if we don't let it move north (constrained by the 'track'), then
>> whatever retarding force we are applying in the east-west direction is
>> translated to the north-south direction against the track. These
forces
>> may increase friction in 'real' bearings, but let's assume 'ideal'
>> bearings so this addtional force against the shaft doesn't slow the
spin
>> of the gyro.
>
> But, from what I understand, w does change as you alter the particle
path
> of the rotor.
>
>> The force against the track in the north-south direction moves through
>> zero distance so no work there. But our retarding force in the
east-west
>> direction is adjusted to allow the shaft to tilt west at something less
>> than one revolution per day so we have a force working through an
angular
>> displacement and have work.
>
> There is a curious phenomena that if you force a gyroscope to move on a
> single axis, it will brake free, stop resisting the torque. I'd
forgotten
> but now recall being there playing with a gyro.
>
> See: Captive (one degree of freedom) gyro
> http://www.upscale.utoronto.ca/IYearLab/gyroscop.pdf
>
Ah HA!!
Yes, this explains it all and now I must admit my earlier statements were
wrong! This is one little thing that was bugging me. Returning to my
example, we try and retard the revolution of the shaft around the track.
It
tries to precess and lift the shaft off the track. So now the *track* is
applying a torque to the shaft at right angle from the torque we were
applying. This second torque effectively tries to make the shaft precess
also, but (and this is the 'mind-warping' part), the direction of
precession
from this side force applied by the track is in the same direction as the
torque we initially applied. It's magnitude is just enough to move the
shaft eastward in the track by just the amount we were trying to restrain
it
from moving westward. It's as if the restraining of the shaft to prevent
precession to the north-south causes the shaft to precess to the east, and
thus there is virtually no torque required to make the shaft stay upright
as
we rotate around the earth in 24 hours (well, some small friction perhaps,
but no significant amount regardless of how large/fast the rotor).
So we can either watch it remain oriented in space and have movement (with
respect to us planet dwellers) with no torque applied, or we can gently
****ge it periodically to remain keep it perfectly upright as the planet
rotates around in 24 hours and have no movement (with respect to us planet
dwellers) and no torque. Either way, no output.
As your link points out, since there is no motion in the north-south
direction, the torque developed in east-west....
T(e-w) = Omega(n-s) X L
No motion n-s, no resisting torque e-w
So a restrained gyro as I was postulating will not generate even the
pitifully small amount of power I calculated before. (learned something
new
today about gyros instead of just getting 24 hours older. Thanks for
sticking with it :-)
> But this seems to creates a contradiction to conservation of angular
> momentum. Spin up a gyro oriented to the poles which transfers momentum
to
> the earth. Push it around on a single axis, broken free from torque, 180
> degrees. Now brake the rotor and you have added even more angular
momentum
> to the earth!??
>
> What am I missing?
If I understand your experiment, you align the shaft parallel to the
earth's
at the north pole and then spin up the rotor (let's say same direction as
the earth for argument's sake). The reaction force of the spin motor will
have slowed the earth a tiny amount. But the interesting part is if we
push
the top of the shaft to the right it will precess away from us and we can
use this to turn the rotor upside down. Now, by simply applying a small
torque to the right of the shaft, we have changed the direction of the
rotor's momentum by 180 degrees.
So, somehow, the reaction force on the planet when we applied that torque
to
the shaft to invert the gyro, must have added /subtracted 2L angular
momentum from the planet.
{Iniitially system momentum was Lplanet1 + Lrotor1 and now total is
Lplanet2
+ Lrotor2. For these two to be equal and assuming the speed of the rotor
is
not diminished ( Lrotor1 = - Lrotor2) Lplanet2 = Lplanet1 +2Lrotor1 }
Interestingly, the total impulse needed to invert the rotor is a constant
if
the rotor's L is constant. A small torque will cause a slow precession
and
have to be applied longer than a high torque that causes a faster
precession.
If we can show that the torque impulse *does* impart 2Lrotor1 momentum to
the planet, then your issue of spinning up / inverting and braking the
rotor
is closed.
I wonder what the effects of that reaction force would be? In theory it
would cause the planet's axis to precess an infitesimal amount 'toward' us
as we push our shaft to the 'right'. Now in our 'ideal thought
experiment',
the shaft and axis are no longer perfectly aligned..... hmm.....
daestrom
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