An approach based on the idea that the spinning nucleus being stretched out along the symmetry axis under the influence of some of centrifugal force has been proposed. The stretching in this work is treated within the framework of quantum mechanics rather than classical mechanics which had been used by Diamond Stephens and Swiatecki. Our approach led to a new formula that describes the dependence of the moment of inertia on the angular momentum. This formula is applied for the calculation of rotational ground state bands of even-even nuclei in the atomic mass range 150 < A < 190 and that having energy ratios in the range between 2.9 < E4 / E2 < 3.33. The results show an overall agreement with the experimental data up to high level energies. There are a small and systematic deviation appears at I > 12 . This deviation increases with the increasing in I and also differs from one nucleus to another.