Why aren't electrical power generators housed in “floating” structures that would allow them to spin?

Every generator I've ever seen is housed in a fixed mount, and uses a rotating magnet in a column, powered by something like combustion, or wind, to generate a current through Faraday induction.

But if you have rotational motion, you get spin acceleration that is orthogonal to the original rotational motion, "for free":

I was wondering if there are generators that use floating columns to take advantage of this additional acceleration.

If not, why?

Is it not enough acceleration to justify the added complexity?

It's a weird property as a general matter, and it depends upon the mass of the rotating object, even if less than all of the mass is rotating. E.g., if you hang a weight from a rotating wheel, the wheel spins faster, even though the weight isn't adding to the rotation of the wheel at all.

It seems to me that, as a result, something like a gyroscopic cage for a generator would allow for significant additional acceleration.

• I use autonomous electrical generators on wheels and if there is such an orthogonal spin, it must be extremely weak in comparison to the weight of the generator because I never noticed anything but vibrations. – Exocytosis May 11 at 21:41

In order to get this precession, you have to apply a torque. In your video, this torque is caused by the weight $$mg$$ of the wheel. The resulting precession rate in this case can be calculated as $$\frac{\mathrm d\phi}{\mathrm dt}=\frac{mgr}{I\omega}$$ Note how the precession rate in the video is increased when the weight is increased by addition of another $$2\ \mathrm{kg}$$.