Effects of Multiple Gyroscopes in Defined Configurations

I have 2 gyroscopes that are aligned on a common plane. The first one is larger than the second and the second resides inside the first. The first one is proportionately less dense to account for it's size and therefore, both discs have the same kinetic energy. Also both gyroscopes are attached to a similar axis with the ability to spin independently, but their orientation in respect to one another is fixed.

Taking these variables into account, if one were to spin each gyroscope in an opposite direction, would they cancel each other out?

In a second configuration, there 3 gyroscopes aligned to an x, y, and z plane at 90 angles to one another and with a common center and locked orientation.

Now if I were to spin the x, y, and z axis clockwise, counter-clockwise, and clockwise what would be the result? How might other rotational setups affect the behavior?

I have no previous knowledge of gyroscopes and I am operating purely on logic. In depth explanations would be appreciated.
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 Quote by GRAYgoose124 I have 2 gyroscopes that are aligned on a common plane. The first one is larger than the second and the second resides inside the first. [...] if one were to spin each gyroscope in an opposite direction, would they cancel each other out?
If the individual angular momenta are opposite then indeed the net angular momentum will be zero.

As I understand your description: the cancelation will be complete because the two centers of mass coincide. To the outside there wil be no angular momentum effects.

A practical example is monorail trains with gyroscopes for active stabilisation. Full size prototypes of such train carriages have actually been built, around 1900. There were two counterrotating flywheels, (positioned side by side) for the purpose of canceling out unwanted effects, and leaving desired effects.

An earlier vehicle, a gyroscopically stabilized car, had a single huge flywheel. (This car didn't have 4 wheels, but just 2). The car readily turned one way, but it was difficult to turn the car the other way.

Anyway, vehicles with active stabilisation from movable flywheels never made it. I suppose the engineering was too complicated, so that none of the designs was economically viable.

 Tags beginner, gyroscope