This paper describes the poloidal and toroidal spin-up of an isothermal plasma in toroidal equilibria. The mechanism is the Stringer spin-up mechanism which will be generalized to an arbitrary toroidal equilibrium using the Hamada coordinate system. Viscous damping or magnetic pumping balances the accelerating forces and determines the threshold of spin-up. The accelerating forces arise from the Coriolis forces which couple the radial flow to the poloidal flow velocity. The theory presented here is a continuation of a previous paper and applies to a multi-species plasma with impurities. In the two-fluid model - or including impurities - in a multi-fluid model, the flux-friction relations derived on every magnetic surface are the basic equations for computing the poloidal and toroidal flow velocities of the particle species. Furthermore, the effect of turbulent forces on the mean flow is analysed. The Reynolds stresses resulting from anisotropic turbulence provide a force in the tangential direction and thus contribute to the poloidal and toroidal spin-up. Furthermore, turbulence increases the Stringer spin-up mechanism and introduces enhanced plasma losses. The final result is a set of differential equations describing the poloidal and toroidal flow on every magnetic surface. The formalism is valid in every regime of collisionality; however, to obtain specific results, appropriate approximations must be found for every regime. This will be outlined for the collisional regime where the viscous forces are given by Braginskii's equations. The relation between plasma rotation and the zonal circulation in planetary atmospheres will be discussed.