An apparatus and method for providing electrical energy to an electrical device by deriving the electrical energy from motion of the device. In one embodiment, the inventive apparatus includes a novel kinetic electrical power generator (KEPG) consisting of an inventive oscillating weight having an internal cavity with a freely movable acceleration element disposed therein, resulting in improved acceleration and oscillation capabilities and lower motion threshold for the weight, a system for converting the weight's oscillating motion into rotational motion, and an electromechanical transducer system for generating electrical energy from the rotational motion. The novel KEPG includes components for modifying the electrical energy for storing and/or feeding the modified electrical energy to the electrical device. Optional components may be included for using the modified electrical energy to recharge one or more rechargeable batteries used in an electric device. Alternate advantageous embodiments of the inventive apparatus include, but are not limited to: a KEPG with multiple inventive oscillating weights to increase velocity and frequency of desirable rotational motion, and a KEPG system utilizing multiple electrically coupled KEPG sub-systems.