Ehrenfest considered an ideal Born-rigid cylinder that is made to rotate. Assuming that the cylinder does not expand or contract, its radius stays the same. But measuring rods laid out along the circumference 2 π π R should be Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the paradox that the rigid measuring rods would have to separate from one another due to Lorentz contraction; the discrepancy noted by Ehrenfest seems to suggest that a rotated Born rigid disk should shatter.