An invariant classification scheme of algebraicallygeneral rotating dust with a purely electric Weyl tensor ispresented. It turns out that the vorticity vector of the dustcongruence is necessarily parallel to a Weyl principal vector, whichis moreover geodesic. An explicit metric expression can be obtainedfor the subclass of expanding models with one functionallyindependent zero-order Riemann invariant. The basic equations forthe general case, where there are two such invariants, are givenwithin a weighted 1+1+2 tetrad formalism.