It is well known that shocks can heat molecular gas, but we are only starting to understand what the consequences might be for galaxy evolution. Observations are now revealing a growing number of galaxies undergoing phases of strong injection of kinetic energy through galaxy interactions or feedback from powerful AGN, which have bright line emission from shock-heated molecular gas that is likely powered by the dissipation of turbulent energy. These observations demonstrate that turbulence – now recognized as an important mechanism regulating star formation – may also be key in regulating galaxy growth. We report on our on-going efforts to quantify the role of molecular gas for the dissipation of kinetic energy through observations on two very different examples, the Antennae galaxy merger and the radio galaxy 3C326 N, a site of strong mechanical AGN feedback. Both galaxies show signatures of strong dissipation of kinetic energy through shocks. We will illustrate how key parameters of these processes like bulk and turbulent velocities, gas masses, and dissipation timescales can be measured with multi-wavelength data, and how this furthers our understanding of how galaxy evolution and star formation in galaxies depend on each other.