The motion of adiabatic jets propagating along the symmetry axis of a Kerr black hole is studied in the case where the outflowing matter possesses angular momentum. A simple parametrization is used for the cross-sectional area of the jets and the results applied to conical and paraboloidal jets. Inclusion of angular momentum in the outflowing material has the effect of shifting the critical point inward closer to the black hole, thus contributing to the radial acceleration of the flow. When the black hole is rotating, this inward shift is more pronounced for direct flows than retrograde ones: for a maximally rotating Kerr hole, the relative shift (with respect to a Schwarzschild black hole) varies from about 12% to 30% for the range of values of angular momentum considered. Rotation in the outflowing matter has the effect of reducing the mass outflow rate. Other parameters being the same, conical jets have their critical points considerably closer to the black hole than paraboloidal jets.