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Dusty-plasma experiments with flat dust clusters are often performed in radio frequency discharges at typical gas pressures of 1 to 100 Pa. For the understanding of the structure and the dynamical behavior of dust clusters, the grain charge and the effective Debye length are of key interest. Direct measurements of these quantities are a challenging task because the dust grains are confined in the plasma-boundary layer, where plasma diagnostics is difficult. Here, we present a new approach to determine the grain charge and the horizontal screening length, which does not require prior knowledge of the plasma parameters. The method is based on a slow and controlled rotation of the neutral-gas column due to a rotating electrode. This leads to centrifugal forces to the dust grains without changing the plasma conditions and allows studying the interparticle distance of a dust cluster as a function of its rotation frequency, which directly depends on the particle charge, the screening length, and the strength of the confining potential.