English: We propose a new derivation of the cranking-model expression for the nuclear collective inertia tensor, introducing explicitly the slow- and fast-motion timescales together with a parameter controlling the interplay between the two modes. The new cranking formula is free from the mass tensor divergencies originating from the nucleon-level crossings in the denominators of the first-order perturbation theory expressions and allows the exploration of the unrestricted deformation space without spurious mass tensor contributions caused by those divergencies. We apply the new formalism without extra parameter adjustments to the collective vibrations in 208Pb.