This is what every flywheel already does (unless it is balanced by a second flywheel going the other way). Conservation of angular momentum: as a flywheel gains

This is what every flywheel already does (unless it is balanced by a second flywheel going the other way). Conservation of angular momentum: as a flywheel gains angular momentum, it must be compensated by the Earth gaining the same amount of angular momentum in the opposite direction. Usually this isn't referred to as "spinning up the Earth" though :-)