In galactic disks, galactic rotation sets the bulk motion of gas, and its energy and momentum can be transferred toward small scales. Additionally, in the interstellar medium, random and noncircular motions arise from stellar feedback, cloud-cloud interactions, and instabilities, among other processes. Our aim is to comprehend to what extent small-scale gas dynamics is decoupled from galactic rotation. We study the relative contributions of galactic rotation and local noncircular motions to the circulation of gas, Γ, a macroscopic measure of local rotation, defined as the line integral of the velocity field around a closed path. We measure the circulation distribution as a function of spatial scale in a set of simulated disk galaxies and model the velocity field as the sum of galactic rotation and a Gaussian random field. The random field is parameterized by a broken power law in Fourier space, with a break at the scale λ_c. We define the spatial scale λ_eq at which galactic rotation and noncircular motions contribute equally to Γ. For our simulated galaxies, the gas dynamics at the scale of molecular clouds is usually dominated by noncircular motions, but in the center of galactic disks galactic rotation is still relevant. Our model shows that the transfer of rotation from large scales breaks at the scale λ_c, and this transition is necessary to reproduce the circulation distribution. We find that λ_eq, and therefore the structure of the gas velocity field, is set by the local conditions of gravitational stability and stellar feedback.