We analyse the role played by shear in regulating star formation in the Galaxy on the scale of individual molecular clouds. The clouds are selected from the 13^CO J=1-0 line of the Galactic Ring Survey. For each cloud, we estimate the shear parameter which describes the ability of density perturbations to grow within the cloud. We find that for almost all molecular clouds considered, there is no evidence that shear is playing a significant role in opposing the effects of self-gravity. We also find that the shear parameter of the clouds does not depend on their position in the Galaxy. Furthermore, we find no correlations between the shear parameter of the clouds with several indicators of their star formation activity. No significant correlation is found between the shear parameter and the star formation efficiency of the clouds which is measured using the ratio of the massive young stellar objects luminosities, measured in the Red MSX survey, to the cloud mass. There are also no significant correlations between the shear parameter and the fraction of their mass that is found in denser clumps which is a proxy for their clump formation efficiency, nor with their level of fragmentation expressed in the number of clumps per unit mass. Our results strongly suggest that shear is playing only a minor role in affecting the rates and efficiencies at which molecular clouds convert their gas into dense cores and thereafter into stars.
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