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 q95, and to decrease with toroidal magnetic field. These results are captured quantitatively by a model of fluctuation entropy balance which gives the Mach number Mi∼=ρ∗/2Ls/LT∼∇Tq95/BT 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