The fastest rotational speed for a disc shaped object was achieved in 1985 . The flywheel was spun up to a tip speed of 1405 m/s, at which point it failed, due to the stresses in the materials involved.
We consider a tower of flywheels, rigidly mounted on top of each other in such a way that the rotational motion of the lower ones is automatically transferred to the ones above, but each flywheel has its own independent source of additional rotational energy, that can give it an extra "kick".
We assume that these flywheels are put in motion in sequence, from bottom to top. Each flywheel is given enough energy in order to put it in rotational motion (same sense of rotation, let's say counterclockwise) with the same angular velocity, on top of what it "inherited" from the lower ones.
For an external observer, assuming a large number of flywheels, is it possible (in principle only because from an engineering perspective it is clearly not feasible) that points on the rim of the topmost flywheel could reach relativistic tangential velocities?
And yes, I must confess, I'm also thinking about Tipler cylinders, but "below" and "above" would translate to "inner" and "outer", and this is not part of the question. It would become a problem of rotational dynamics.
Edit. Added question. Could these systems of connected flywheels store energy more efficiently,?