The controlled rotation of acoustically levitated samples is beneficial for analyzing sample properties, e.g., in a recently reported room temperature x-ray diffraction experiment, wherein thin film sample holders comprising thin film disks with short blades attached around their circumference were utilized. However, the mechanism of producing the torque and the determinant factor of the rotation direction for these planar ultrasonic rotors have been elusive. We, therefore, study the impact of the size and shape on the rotation characteristics of these ultrasonic rotors in air and further study the influence of the viscosity of fluid. Theory and experiment demonstrate the essential role of the short blades in producing the acoustic torque both in air and water. In the airborne case, the shape and arrangement of the blades are found to determine the rotation direction. In water, with a dynamic viscosity 55 times higher than that of air, we demonstrate that ultrasonic rotors down to 25-μm-disk-diameter function in an optimized experimental geometry with approximately the same actuation efficiency as in air. Our results will be beneficial to further improve the applicability of the ultrasonic rotors as sample holders for airborne experiments and to explore the micrometer-scale ultrasonic rotors in liquid.