The industrial-scale rotating drums are usually operated in the rolling or slumping mode. For the rolling mode, the granular material bed can be divided into two regions, namely, a 'passive' region where particles are carried up by the drum wall, and an 'active' region where particles cascade down. As solids mixing mainly occurs in the active region, solids motion in this region and solids exchange between the active and passive regions are of prime importance for the overall performance of the drum. This paper reports some observations on particle motion in the transverse plane of a three-dimensional relating drum operated at low and medium rotational speeds. The non-invasive PEPT (positron emission particle tracking) technique is used to follow particle trajectory and velocity. A mathematical model based on the thin-layer approximation is proposed to describe solids motion in the active layer. Reasonable agreement between the model predictions and experiments is obtained. A new parameter termed the 'solids exchange coefficient' is proposed to characterise particle exchange between the passive and active regions. A theoretical expression for this parameter is also derived. This expression, upon application of the thin-layer approximation, is reduced to give an explicit relationship between the solids exchange coefficient and drum operating parameters such as rotational speed and fill percentage. as well as the bed material theological properties. The solids exchange coefficient is also shown to give a possible scale-up rule for rotating drums operated in a rolling mode.