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

Wormhole solutions sourced by fluids, I: Two-fluid charged sources