This problem is a combination of several problems I've posted in this
group. When I combine the problems, the answers given to me in
previous posts don't work. Here's the problem.

I have two frames which I will call the stationary frame and the
moving frame. Their relative velocity is 0.866 c. In the stationary
frame, parallel to the x-axis there is a rod and a rotating cylinder.
The end points of the rod and the rotating cylinder are at the same x
coordinates. The diameter of the cylinder is 10 meters and the
cylinder is rotating at 10 revolutions per second.

As measured in the moving frame, let the length of the rod and the
length of the rotating cylinder be 1 light-second. At time t0 as
measured in the moving frame, each point of the rod is simultaneously
attached to the surface of the rotating cylinder. (Assume the rod is
made of a material that is very malleable).

As viewed in the stationary frame, one end of the rod was attached to
the rotating cylinder 1.73 seconds before the other end. That means
that the rod wrapped around the cylinder about 17 times in a spiral
pattern. (The moving frame measures the attached rod to be a straight
line at any instant of time as measured in the moving frame).

We let the attached rod and cylinder rotate for however long is
necessary to achieve a steady-state condition for the shape of the
rod. We then change the chemical composition of the attached rod so
that it is no longer malleable. It becomes rigid and fixed in that
shape and requires an extremely large force to change its shape.

Now, after this occurs, at time t1 as measured in the moving frame,
each attachment point which connects the rod to the rotating cylinder
is eliminated so that the rod is no longer attached to the cylinder.
Let's say this occurs at the instant (as measured in the moving frame)
when all the y coordinates of the rod are zero so that the rod begins
moving only in the X-Y plane. Observers in the moving frame measure a
straight rod traveling in the X-Y plane, and this rod has zero
rotation rate.

Using Einstein's notions, I don't see how to explain things from the
point of view of observers in the stationary frame. In this frame,
the rod is a rigid spiral wrapped 17 times around a cylinder. When
the contact with the cylinder is eliminated, there must be some force
which straightens the spiral shaped rod as the rod is unwrapped from
the cylinder, and this must occur in 1.73 seconds. When the rod was
initially wrapped around the cylinder, this force came from the
cylinder and the force required was minimal since the rod was
extremely malleable at that time (the given information). However, in
unwrapping the rod from the cylinder, the force comes from the
chemical bonds throughout the rod. The force is applied through
chemical bonds, and the contact points are eliminated far faster than
any chemical bond can react. So how can you make the views in the two
frames agree?
David Seppala

Please note: If you don't know the physics answer, please feel free
to put up a post that includes personal attacks of my intelligence and
education. That's the approach used by the vast majority of the
people on the planet when they can't logically explain something, so
why should you be different? Besides, your peers may join in giving
each of you mutual support.