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This research focuses on studying the scattering phenomenon. Scattering electromagnetic waves from a rotating conducting cylinder is investigated when the material of the conducting cylinder is linear, homogeneous, isotropic, and dispersive. This study is an extension of a previous work that investigated the effect of the rotating conducting cylinder on the scattered phase and amplitude, when the material of the conducting cylinder is linear, homogeneous, isotropic, and nondispersive. One of the important result of the previous work is that the Franklin transformation is a proper and more accurate method to calculate the effect of the rotation, and gives more accurate results than Galilean transformation. In this research, the Franklin transformation will be used to investigate the effect of the rotation of the object on the scattered phase and magnitude of the incident waves. The two types of incident waves (E-wave and H-wave) will be considered herein. The simulation results will clearly display the behavior of the scattered phase and magnitude with changes to the incident frequency, the speed of rotation, and the radius of the very good conducting cylinder. Moreover, this result is compared with the result of the previous work (non- dispersive material) to show the behavior of the scattered phase and magnitude when the incident frequency, speed of the rotation and radius of the very good conducting cylinder is changed.