  We consider stationary rotating cylindrically symmetric dust spacetimes. We
first show that the Maitra spacetime is the unique non-rigidly (non null shear
scalar) rotating solution with a regular axis and that is the most general one
of the field equations. We are also able to demonstrate what Maitra's paper
does not show, where the solution is merely stated without any demonstration.
Then we find that the non-rigidly rotating spacetimes, not necessarily regular,
can be matched, across timelike cylindrical hypersurfaces, to a one-parameter
family of stationary vacuum exteriors given by the Weyl class but not to the
Lewis class, generalizing a result by Bonnor and Steidman. Among other
properties, it is shown that the amount of rotating dust packed inside a
cylinder is bigger if it is rigidly rotating than non-rigidly rotating.
Finally, we show that in the non-rigidly rotating cases the fluid necessarily
has vorticity and the spacetimes are not silent, where the magnetic part of the
Weyl tensor is non-zero.
