The interplay between the proton-alpha-particle differential flow speed, vαp, and angular momentum transport in the solar wind is explored by using a three-fluid model. The force introduced by the azimuthal components is found to play an important role in the force balance for ions in interplanetary space, bringing the radial flow speeds of protons and alpha particles closer to each other. For the fast solar wind, the model cannot account for the decrease of vαp observed by Helios between 0.3 and 1 AU. However, it can reproduce the vαp profile measured by Ulysses beyond 2 AU, if the right value for vαp is imposed at that distance. In the slow wind, the effect of solar rotation is more pronounced if one starts with the value measured by Helios at 0.3 AU: a relative change of 10%-16% is introduced in the radial speed of the alpha particles between 1 and 4 AU. The model calculations show that, although alpha particles consume only a small fraction of the energy and linear momentum fluxes of protons, they cannot be neglected when considering the proton angular momentum flux Lp. In most examples, it is found that Lp is determined by v αp for both the fast and the slow wind. In the slow solar wind, the proton and alpha particle angular momentum fluxes Lp and L α can be several times larger in magnitude than the flux carried by the magnetic stresses LM. While the sum Lp = Lp + Lα is smaller than LM, for the modeled fast and slow wind alike, this result is at variance with the Helios measurements.