  Stars form in the densest regions of molecular clouds, however, there is no
universal understanding of the factors that regulate cloud dynamics and their
influence on the gas-to-stars conversion. This study considers the impact of
Galactic shear on the rotation of giant molecular clouds (GMCs) and its
relation to the solenoidal modes of turbulence. We estimate the direction of
rotation for a large sample of clouds in the \ce{^{13}CO}/\ce{C^{18}O} (3-2)
Heterodyne Inner Milky Way Plane Survey (CHIMPS) and their corresponding
sources in a new segmentation of the \ce{^{12}CO}(3-2) High-Resolution Survey
(COHRS). To quantify the strength of shear, we introduce a parameter that
describes the shear's ability to disrupt growing density perturbations within
the cloud. Although we find no correlation between the direction of cloud
rotation, the shear parameter, and the magnitude of the velocity gradient, the
solenoidal fraction of the turbulence in the CHIMPS sample is positively
correlated with the shear parameter and behaves similarly when plotted over
Galactocentric distance. GMCs may thus not be large or long-lived enough to be
affected by shear to the point of showing rotational alignment. In theory,
Galactic shear can facilitate the rise of solenoidal turbulence and thus
contribute to suppressing star formation. These results also suggest that the
rotation of clouds is not strictly related to the overall rotation of the disc,
but is more likely to be the imprint of Kelvin-Helmholtz instabilities in the
colliding flows that formed the clouds.
