The amount of spin-up over time for clouds shaped as partial annuli and spheres. Left: simulated prograde spin-up of clouds in the shape of partial annuli that orbit around a central mass with (blue, SG) and without (red, NSG, Eq. (14)) self-gravity enabled. When self-gravity and collisions are included, the prograde spin-up levels off around the free-fall timescale (plotted here for an equivalent sphere), when cloud shear comes to a halt. Right: same calculation, computed with spherical clouds and varying initial densities. Their initial rotation scales as L₀ ∝ (R_cl/R_H)², whereas the prograde spin-up during their collapse scales as L_rot ∝ (R_cl/R_H)⁵ (see Sect. 2.3). As a result, sparse clouds with R_cl ≃ R_H accumulate most of their rotation during their collapse, whereas the rotation of denser clouds remains largely unchanged.