Changes in the core intrinsic toroidal rotation velocity following L- to H- and L- to I-mode transitions have been investigated in Alcator C-Mod tokamak plasmas. The magnitude of the co-current rotation increments is found to increase with the pedestal temperature gradient and ##IMG## [http://ej.iop.org/images/0029-5515/57/11/116004/nfaa7b44ieqn001.gif] {$q_{95}$} , and to decrease with toroidal magnetic field. These results are captured quantitatively by a model of fluctuation entropy balance which gives the Mach number ##IMG## [http://ej.iop.org/images/0029-5515/57/11/116004/nfaa7b44ieqn002.gif] {$M_i \cong \rho _*/2 L_s/L_T \sim \nabla T q_{95}/B_{T}$} in an ITG turbulence dominant regime. The agreement between experiment and theory gives confidence for extrapolation to future devices in similar operational regimes. Core thermal Mach numbers of  ∼0.07 and  ∼0.2 are expected for ITER and ARC, respectively.