  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.
