  We briefly discuss some of the known and new properties of rotating
geometries that are relevant to this work. We generalize the analytical method
of superposition of fields, known for generating nonrotating solutions, and
apply it to construct massless and massive rotating physical wormholes sourced
by a source-free electromagnetic field and an exotic fluid both anisotropic.
Their stress-energy tensors are presented in compact and general forms. For the
massive rotating wormholes there exists a mass-charge constraint yielding
almost no more dragging effects than ordinary stars. There are conical spirals
through the throat along which no local negative energy densities are noticed
for these rotating wormholes. This conclusion extends to nonrotating massive
type I wormholes derived previously by the author that seem to be the first
kind of nonrotating wormholes with this property. Based on the classification
made in J. Cosmol. Astropart. Phys. 07 (2015) 037 [arXiv:1412.8282]: "Type I
wormholes have their radial pressure dying out faster, as one moves away from
the throat, than any other component of the stress-energy and thus violate the
least the local energy conditions. In type II (resp. III) the radial and
transverse pressures are asymptotically proportional and die out faster (resp.
slower) than the energy density".
