  Asteroids, planets, stars in some open clusters, as well as molecular clouds
appear to possess a preferential spin-orbit alignment, pointing to shared
processes that tie their rotation at birth to larger parent structures. We
present a new mechanism that describes how collections of particles or 'clouds'
gain a prograde rotational component when they collapse or contract while
subject to an external, central force. The effect is geometric in origin, as
relative shear on curved orbits moves their shared center-of-mass slightly
inward and toward the external potential during a collapse, exchanging orbital
angular momentum into aligned (prograde) rotation. We perform illustrative
analytical and N-body calculations to show that this process of prograde
spin-up proceeds quadratically in time ($\delta L_\mathrm{rot} \propto t^2$)
until the collapse nears completion. The total rotational gain increases with
the size of the cloud prior to its collapse: $\delta
L_\mathrm{rot}/L_\mathrm{H} \propto (R_\mathrm{cl}/R_\mathrm{H})^5$, and
typically with distance to the source of the potential ($L_\mathrm{H}\propto
r_0)$. For clouds that form at the interface of shear and self-gravity
($R_\mathrm{cl} \sim R_\mathrm{H}$), prograde spin-up means that even setups
with large initial retrograde rotation collapse to form prograde-spinning
objects. Being a geometric effect, prograde spin-up persists around any central
potential that triggers shear, even those where the shear is strongly
retrograde. We highlight an application to the Solar System, where prograde
spin-up can explain the frequency of binary objects in the Kuiper belt with
prograde rotation.
