Building upon recent advancements in linear electroadhesive clutch materials and performance, this paper examines the feasibility of a self-reinforcing electroadhesive rotational clutch using a simple model. The design aims to deliver improvements in applications where performance is limited by the torque-to-power and torque-to-mass ratios offered by conventional electromagnetic or magnetorheological clutches. The performance of the self-reinforcing design is related to the device's geometric parameters and hence the robustness of clutch configurations is examined by modeling the system parameters as having stochastic properties. A design example based on the clutch requirements of a gyroscopic balance assistance device is analyzed. The analysis predicts that substantial improvements in torque-to-power and torque-to-mass ratios are possible with the presented design compared to industry-leading rotational clutches.