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We investigate the origin of the observed scaling $j\sim R^{3/2}$ between thespecific angular momentum $j$ and the radius $R$ of molecular clouds (MCs) andtheir their substructures, and of the observed near independence of $\beta$,the ratio of rotational to gravitational energy, from $R$. To this end, wemeasure the angular momentum (AM) of sets of particles in an SPH simulation ofthe formation, collapse and fragmentation of giant MCs. The sets of SPHparticles are defined either as ``clumps'' (connected particle sets), or aslagrangian sets that conform a connected clump only at a certain time $\tdef$.We find that: {\it i)} Clumps evolve along the observed \jR\ relation at alltimes, {\it ii)} Lagrangian particle sets evolve along the observed relationwhen the volume containing them also contains a large number of other``intruder'' particles. Otherwise, they evolve with $j\sim$ cst. {\it iii)}Tracking lagrangian sets to the future, we find that a subset of the SPHparticles participates in the collapse, while another disperses away. {\it iv)}Noting that, under AM conservation, $\beta$ increases during contraction, wesuggest that its near independence of radius may arise from the competitionbetween this increase and an increase in the AM exchange rate at higherrotational energy density gradient. {\it v)} We suggest that, if MCs areglobally dominated by gravity, the observed \jR\ relation arises because theobservational selection of its dense structures amounts to selecting thefragments that have lost AM via Reynolds stresses from their neighbors.

Evolution of the angular momentum during gravitational fragmentation of molecular clouds