When a magnetic field is turned on, a superconducting body acquires an angular momentum in direction opposite to the applied field. This gyromagnetic effect has been established experimentally and is understood theoretically. However, the corresponding situation when a superconductor is cooled in a pre-existent field has not been examined. We argue that the conventional theory of superconductivity does not provide a prediction for the outcome of that experiment that does not violate fundamental laws of physics, either Lenz's law or conservation of angular momentum. The theory of hole superconductivity predicts an outcome of this experiment consistent with the laws of physics.