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Most neutron capture elements have a double production by r- and s-processes, but the question of production sites is complex and still open. Recent studies show that including stellar rotation can have a deep impact on nucleosynthesis. We studied the evolution of Sr and Ba in the Milky Way. A chemical evolution model was employed to reproduce the Galactic enrichment. We tested two different nucleosynthesis prescriptions for s-process in massive stars, adopted from the Geneva group and the Rome group. Rotation was taken into account, studying the effects of stars without rotation or rotating with different velocities. We also tested different production sites for the r-process: magneto rotational driven supernovae and neutron star mergers. The evolution of the abundances of Sr and Ba is well reproduced. The comparison with the most recent observations shows that stellar rotation is a good assumption, but excessive velocities result in overproduction of these elements. In particular, the predicted evolution of the [Sr/Ba] ratio at low metallicity does not explain the data at best if rotation is not included. Adopting different rotational velocities for different stellar mass and metallicity better explains the observed trends. Despite the differences between the two sets of adopted stellar models, both show a better agreement with the data assuming an increase of rotational velocity towards low metallicity. Assuming different r-process sources does not alter this conclusion. [ABSTRACT FROM AUTHOR]