The density of rime ice accreted on a target moving through a cloud of supercooled water droplets has been measured in order to determine whether the rime density, or other characteristics, are modified by radial forces. Two similar targets in the same cloud were rotated on frames that provided the same speed but different radial accelerations to each target. The mass accreted and the rime density were found to be significantly reduced under high radial forces. A relationship was determined between rime density, the mean volume droplet size, the speed, the temperature and the acceleration. These results are important to the design of liquid-water content measurement equipment, particularly for laboratory use, where the mass of ice accreted by a target on a rotating frame is determined. The results also have relevance to laboratory measurements of electric charge transfer between riming targets and re-bounding ice crystals.