mounstable rants concerning Instability of long cylinders

Magnetic bearings, eh? OK.

Here's what you do: you take your two twenty mile long, four mile wide
cylinders, and you lop one endcap off each (actually, it'd probably
be best to just not build those two endcaps in the first place).
Place the two cylinders end to end, about a mile apart. Then you take
a one mile long cylinder (still four miles wide) and attach it with
your magnetic bearings to the two cylinders.

Now do the usual filling with air, landscaping, and so on. At the end
of your big cylinder which connects to your non-rotating connector,
have that sci-fi cliche, a moving sidewalk. The slidewalk has hand
rails and is not moving when you step aboard. It wraps around the
whole 12.566370614359172953850573533118 mile circumference. Once you
get aboard it, grab the hand rails and be "de-spun" so that you step
into the non-rotating section without injury. You now have a four
mile wide, one mile long zero-G playground and/or work center. Use
another slidewalk to "re-spin" in the opposite direction if you want
to enter the other cylinder.

That number, 12.566370614359172953850573533118, now that's
interesting. We could play with that. But first, what do you think
of my connector thing-a-ma-bob?