We investigate the role of radiation pressure in accelerating the broad absorption line (BAL) outflows in QSOs by comparing their properties with those of radiatively driven O star winds. We find that, owing to their lower column densities and higher velocity spreads, BAL outflows have only a few tens of strong resonance lines that are dynamically important, as compared with 10(exp 3) - 10(exp 4) lines in O star winds. We show that the combined radiative force (the 'force multiplier') declines more rapidly as a function of column density for BAL outflows than for O star winds. This is mainly attributed to the absence of lines from excited states in the BAL region. The absorbing gas in BAL outflows must have a small filling factor in order for radiative acceleration to be important dynamically. This allows the absorbing material to remain at a high enough density to maintain the ion species necessary for efficient radiative acceleration as well (as those responsible for the observed absorption), without the average flow density becoming so large that the absorbing matter cannot be accelerated by an increment larger than its own sound speed. The latter condition is necessary if the outflow is to tap a large portion of the incident photon momentum. Once a small filling factor is assumed, radiative acceleration can be more efficient in BAL outflows than in O stars. We show that terminal velocities of a few times 10(exp 4) km/sec can be expected, provided that the absorbing matter does not have to drag with it a much heavier substrate.