The composition (φ) and temperature dependence (T) of the monomeric friction factor (ζ) has been examined for styrene (S) and methyl methacrylate (MMA) in five SMMA diblock copolymers and the corresponding homopolymers. In all cases the degree of polymerization was approximately 150, sufficiently low to ensure that the chain dynamics follow the Rouse model and that the copolymers are far above the order-disorder transition. The five diblock copolymers had styrene compositions of 91, 70, 39, 19, and 9 wt %. Values of an effective friction factor, ζeff, were obtained from measurements of the steady flow viscosity via the Rouse model, whereby ζeff represents an average over the S and MMA contributions. Values of the component friction factors, ζPS and ζPMMA, were extracted from forced Rayleigh scattering tracer diffusion measurements of dye-labeled PS, PMMA, and SMMA chains. In accord with previous studies, ζPMMA in pure PMMA is significantly greater than ζPS in pure PS, whether compared at equal T or equal T - Tg, an effect attributable to specific details of local relaxation in PMMA. This difference between ζPMMA and ζPS persists in a common SMMA matrix, an effect which can be quantitatively accounted for by the recently introduced, concept of self-concentration. The values of ζeff increase monotonically with MMA content at fixed T and with decreasing T at fixed φ. The φ dependence of ζeff is consistent with both "Rouse" and "Arrhenius" mixing rules, utilizing the pure component friction factors as input. The T dependence of ζeff follows the standard Williams-Landel-Ferry relation, but the data for different φ do not collapse to a single curve when plotted against T - Tg. In this respect, the PS/PMMA system is more complicated than the previously studied PS/polyisoprene system.