Found this cartoon on the internet.
How can we explain this does not happens?
Nothing can go faster than the speed of light.
One of the explanation I can think of is that there will be the change of the rotational inertia, so to preserve the momentum of inertia the rotational speed will be much slower than the original.
It will be impossible to make a massless rigid stick, because of the huge inertia caused by the rotation. So the change of the rotational intertia will be inevitable.
What do you think?