The rotation rate of the solar radiative zone is an important diagnostic for angular momentum transport in the tachocline and below. In this paper, we study the contribution of viscous and magnetic stresses to the global angular momentum balance. By considering a simple linearized toy model, we discuss the effects of field geometry and applied boundary conditions on the predicted rotation profile and rotation rate of the radiative interior. We compare these analytical predictions with fully nonlinear simulations of the dynamics of the radiative interior, as well as with observations. We discuss the implications of these results as constraints on models of the solar interior.