The rotational properties of numerical models of centrally condensed , turbulent molecular cloud cores with velocity fields that are characterized by Gaussian random fields are investigated .
It is shown that the observed line width – size relationship can be reproduced if the velocity power spectrum is a power-law with P ( k ) \propto k ^ { n } and n = -3 to -4 .
The line-of-sight velocity maps of these cores show velocity gradients that can be interpreted as rotation .
For n = -4 , the deduced values of angular velocity \Omega = 1.6 km s ^ { -1 } pc ^ { -1 } \times ( R/0.1 pc ) ^ { -0.5 } and the scaling relations between \Omega and the core radius R are in very good agreement with the observations .
As a result of the dominance of long wavelength modes , the cores also have a net specific angular momentum with an average value of J / M = 7 \times 10 ^ { 20 } \times ( R /0.1 pc ) ^ { 1.5 } cm ^ { 2 } s ^ { -1 } with a large spread .
Their internal dimensionless rotational parameter is \beta \approx 0.03 , independent of the scale radius R .
In general , the line-of-sight velocity gradient of an individual turbulent core does not provide a good estimate of its internal specific angular momentum .
We find however that the distribution of the specific angular momenta of a large sample of cores which are described by the same power spectrum can be determined very accurately from the distribution of their line-of-sight velocity gradients \Omega using the simple formula j = p \Omega R ^ { 2 } where p depends on the density distribution of the core and has to be determined from a Monte-Carlo study .
Our results show that for centrally condensed cores the intrinsic angular momentum is overestimated by a factor of 2-3 if p = 0.4 is used .