The omnipresence of rotation, often observed in its own rest frame of reference, profoundly affects human experience, science and technology. Here, the authors develop a formulation governing the rest frame electrodynamics in rotating electromagnetic systems and circuits. This study reveals new rotation-induced effects such as fictitious charges, gain, energy harvesting, and new device functionalities, e.g., positive or negative memristors and their dualities. These effects may potentially offer pathways to new technologies and materials.