A rigid plate end-effector at the tip of a high-speed manipulator can remotely manipulate an object without grasping it. This paper discusses a dynamic nonprehensile manipulation strategy to rotate thin deformable objects on a rigid plate with two degrees of freedom (DOFs). The deformation of the object due to dynamic effects is exploited to produce fast and stable rotation. By varying the frequency of the rotational component of the plate's motion, we show that the dynamic behavior of the object mimics either a sliding, walking, or running gait of a biped. We introduce a model to simulate this type of system in which the object is constructed of multiple nodes that are connected by viscoelastic joint units with three DOFs. The joint's viscoelastic parameters are estimated experimentally in order to model real food. Afterward, simulation analysis is used to investigate how the object's rotational behavior and its angular velocity change with respect to the plate's motion frequency. We show how the object's behavior during rotation is analogous to bipedal sliding, walking, and running gaits and then obtain optimal plate motions leading to the maximal angular velocity of the object. We also reveal that an appropriate angular acceleration of the plate is essential for a dynamically stable and fast object's rotation. We further show that the friction coefficient that maximizes the object's angular velocity depends on its gait.