More on gyroscopic behaviours

[THX-1138]

Posit a flywheel as a gyroscope, rotating clockwise

Now consider the flywheel pierced at regular intervals aeound the circumference, and in each piercing there is another gyroscope rotating widdershins. and that the sum of their angular momentums is equal but opposite to that of the larger flywheel.

[latex]\sum_{1}^{4} L(small~gyro~n) = - L (large~gyro)[/latex]

What behaviours or peculiarities could be expected from such a framework, even before force was applied to the [latex]Z[/latex] axis?

Edited November 6, 2018 by THX-1138
typo

[studiot]

17 minutes ago, THX-1138 said:

Posit a flywheel as a gyroscope, rotating clockwise

This does not conform to the standard definition of a gyroscope

Quote

Stephenson

A gyroscope is any symmetrical spinning body, whose axis of rotation is also free to rotate about some point.

 

Edited November 6, 2018 by studiot

[THX-1138]

The larger wheel and its spindle are one piece, and are spinning; assume frictionless bearings for normal conditions.  The bearings of the smaller gyroscopes' spindles are fixed to the larger wheel, but the wheels themselves are free to rotate upon those spindles.

[studiot]

23 minutes ago, studiot said:

41 minutes ago, THX-1138 said:

Posit a flywheel as a gyroscope, rotating clockwise

This does not conform to the standard definition of a gyroscope

 

Please answer my comment.

[THX-1138]

Replace 'flywheel' with 'fairly massive disc,' and 'counterclockwise' with 'counterclockwise when viewed from above.'

[studiot]

I will try one last time to inject some sense into this thread.

 

The large disk (flywheel is an OK term, it is just not a gyroscope) is rotating about its central axis as you have shown.

Since the small disks are stated to be mounted in the large disk, they will be rotating with it in the same direction as the large disk, in addition to their own contra motion.

So they will contribute a significant amount to the total clockwise inertai about the central large disk pivot.

 

But your have carefully avoided showing the axes of the small disks rotating the other way.

These axes do not coincide with the rotational axis of the large disk so I will leave it as a mathematical exercise to show how their motions about parallel axes add so the total is zero.

Hint as you have drawn your diagram, the top and bottom effects and the left and right effects from the small disks rotations will cancel since they are on opposite sides of the central axis of the big disk.

[THX-1138]

Actually, the grey circles show the direction of rotation to be contra to that of the larger wheel; it didn't come out clearly in the diagram, I guess. The axes of the smaller gyroscopes are parallel to that of the larger one; they are all parallel to the [latex]Y[/latex] axis. AND I clearly stated that the small discs were rotating contra  to the large one (widdershins vs clockwise).

I am not a mathematician, so my gut feeling is that, since there are no precessional forces at play when the experiment is in its unstressed state, all of the gyroscopes having parallel axes, so my first question would be about that behaviour, and the effect of altering rotational velocities.

The diagram is a top-down view.  I'll take your word that 'effects' would cancel out on opposite sides of the large disk.  Which effects, though?  And what would happen if force were applied to, say, rotate the structure around the [latex]X[/latex] axis?

[studiot]

Try this experiment.

 

Take a sheet of paper and place it flat on the desk.

Place two fingers of one hand close together near one corner and twist the paper so it rotates on the desk.

Which part of the paper stays still and which part moves the most?

Now remove the first hand and place two fingers of the other hand near the corner diagonally opposite the first one.

Rotate again in the same sense.

Again note which part of the paper moves and which remains still.

Now try both hands at once.

What happens to the sheet of paper?

[THX-1138]

Since both hands are holding down the paper at opposite corners, it's not going to move (at least not without some wrinkling, tearing, or other out-of-scope effects).

So I have this contraption spinning with some moderate rate of RPMs, and I'm holding it by the bearings of the main spindle.  I try to change its angle (say I push down with my left hand and up with my right).  What will happen?

[Externet]

Like the flywheel being attached to the central shaft ?

 

[quiet]

Let go slowly.

- A gyro don't exert opposition to parallel translation of it's axis. If you try change the direction of the axis, opposition appears.

- Think the following. With the large wheel in rest, the four little wheels are spinning. Later, with the small wheels spinning, the large wheel start rotation. This rotation causes parallel translation of the axis of the each little wheel. This kind of translation don't receive opposition from the little gyros. Then, except the mass, there isn't no influence of the little gyros on the rotation of the big wheel.

As I see the situation, the main question is the following. With the system like was described in the initial post of the thread, if we try to change the axis direction of the big wheel, what will happen? Will we find opposition or not?

 

Edited December 17, 2018 by quiet