An inertial unit comprising an inertial core (3) that is connected to a control unit (50) and that includes three gyros (9, 10, 11) that are mounted relative to one another so as to have sensing axes (X, Y, Z) that are substantially perpendicular to one another, the gyros being vibrating axisymmetric gyros with hemispherical resonators, the unit being characterized in that the core is mounted on a carousel (2) arranged to drive the inertial core in rotation about an axis of rotation (4) at at least one frequency that corresponds to a minimum for spectral error density of the gyros. An angle-measurement method making use of the unit.