  We investigate numerically and semi-analytically the collapse of low-mass,
rotating prestellar cores. Initially, the cores are in approximate equilibrium
with low rotation (the initial ratio of thermal to gravitational energy is
$\alpha_0 \simeq 0.5$, and the initial ratio of rotational to gravitational
energy is $\beta_0 = 0.02 {\rm to} 0.05$). They are then subjected to a steady
increase in external pressure. Fragmentation is promoted -- in the sense that
more protostars are formed -- both by more rapid compression, and by higher
rotation (larger $\beta_0$). In general, the large-scale collapse is
non-homologous, and follows the pattern described in Paper I for non-rotating
clouds, viz. a compression wave is driven into the cloud, thereby increasing
the density and the inflow velocity. The effects of rotation become important
at the centre, where the material with low angular momentum forms a central
primary protostar (CPP), whilst the material with higher angular momentum forms
an accretion disc around the CPP. More rapid compression drives a stronger
compression wave and delivers material more rapidly into the outer parts of the
disc.
