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We present high spatial resolution (12pc) Atacama LargeMillimeter/sub-millimeter Array CO(J=3-2) observations of the nearby lenticulargalaxy NGC4429. We identify 217 giant molecular clouds within the 450pc radiusmolecular gas disc. The clouds generally have smaller sizes and masses buthigher surface densities and observed linewidths than those of Milky Way discclouds. An unusually steep size - line width relation and large cloud internalvelocity gradients (0.05 - 0.91 km s^-1 pc^-1) and observed Virial parameters(alpha_obs,vir = 4.0) are found, that appear due to internal rotation driven bythe background galactic gravitational potential. Removing this rotation, aninternal Virial equilibrium appears to be established between theself-gravitational (Usg) and turbulent kinetic (Eturb) energies of each cloud,i.e. alpha_sg,vir=Usg/Eturb = 1.3. However, to properly account for both selfand external gravity (shear and tidal forces), we formulate a modified Virialtheorem and define an effective Virial parameter alpha_eff,vir = alpha_sg,vir +Usg/Eext (and associated effective velocity dispersion). The NGC4429 cloudsthen appear to be in a critical state in which the self-gravitational energyand the contribution of external gravity to the cloud's energy budget (Eext)are approximately equal, i.e. Eext/Usg~1. As such, alpha_eff,vir = 2.2 and mostclouds are not virialised but remain marginally gravitationally bound. We showthis is consistent with the clouds having sizes similar to their tidal radiiand being generally radially elongated. External gravity is thus as importantas self-gravity to regulate the clouds of NGC4429.

WISDOM Project -- IX Giant Molecular Clouds in the Lenticular Galaxy NGC4429: Effects of Shear and Tidal Forces on Clouds