  We investigate magnetization induced by mechanical rotation, known as the
Barnett effect, in the two-dimensional electron gas. The energy eigenvalues of
the rotating system (Barnett levels) are non-degenerate, thereby differ from
Landau levels in the presence of a magnetic field. The magnetic response caused
by the coupling of the Barnett gauge field to both the electron spin and
orbital degree of freedom is found to be paramagnetic. Surprisingly, rotation
does not cause any charge redistribution, i.e. in the two-dimensional electron
gas centrifugal forces are quantum mechanically suppressed.
