  The present work attempts to analytically explain the effects on the moment
of inertia, $I$, caused by the evolution of stellar velocity in main-sequence
stars. We have found that the effects linked to stellar oblateness can be
estimated from the variation of the magnetic braking index denoted by $\Delta
q$. We have also found that the effect of $\dot{I}$ is here a determining
factor for understanding the delicate mechanisms that control the spin-down of
stars in this evolutionary phase. We note that our models predict that the
behaviour of the variations of the braking index is distinct when the star
density decreases. In the present study, we used three sample stellar targets
from the archives of the different satellites, such as CoRoT and
\textit{Kepler}, to estimate the possible correlations among the parameters
extracted from our model and the stellar age. As a result, we find that $\Delta
q$ is strongly correlated to the age of stars. In conclusion, we suggest that
the variations of the magnetic braking index due to oblateness can be an
interesting way to estimate stellar ages.
