Many strongly correlated electronic materials have a domain structure that greatly influences the bulk properties and obscures the fundamental properties of the homogeneous material. Nanoscale samples, on the other hand, can be smaller than the characteristic domain size, thus making it possible to explore these fundamental properties in detail. Here, we report new aspects of the metal-insulator transition(1-3), studied in single-domain vanadium dioxide nanobeams(4-6). We have observed supercooling of the metallic phase by 50 degrees C, an activation energy in the insulating phase that is consistent with the optical gap, and a connection between the metal-insulator transition and the equilibrium carrier density in the insulating phase. Our devices also provide a nanomechanical method for determining the transition temperature, enable measurements on individual metal-insulator interphase walls to be made, and allow general investigations of phase transitions in quasi-one-dimensional geometries.