Poly(methyl methacrylate) (PMMA)-C-60 nanocomposites, with compositions in the range 0 <= phi(wt)(C60) <= 0.05, are shown to exhibit systematic increases in dynamic shear moduli, in glass transition temperature (T-g), and in the longest relaxation time of the polymer (tau(R)) with increasing fullerene concentration. We show that while the phi(wt)(C60) dependence of the plateau modulus can be reconciled with a conventional "filler" effect, the systematic increases in T-g and in tau(R) are associated with specific interactions between the C-60 and the polymer segments. In the melt, these segment-C-60 interactions are proposed to reduce polymer segmental mobility in the vicinity of the particle surface and ultimately suppress polymer dynamics, as measured mechanically, in a manner consistent with an increase in the polymer segmental friction coefficient.