  We have analyzed the rotational properties of 12 clumps using $^{13}$CO
(1--0) and C$^{18}$O (1--0) maps of the Five College Radio Astronomy
Observatory 13.7 m radio telescope. The clumps, located within molecular
clouds, have radii ($R$) in the range of 0.06 -- 0.27\,pc. The direction of
clump elongation is not correlated with the direction of the velocity gradient.
We measured the specific angular momentum (J/M) to be between 0.0022 and 0.025
pc\,km\,s$^{-1}$ based on $^{13}$CO images, and between 0.0025 and 0.021
pc\,km\,s$^{-1}$ based on C$^{18}$O images. The consistency of $J/M$ based on
different tracers indicates the $^{13}$CO and C$^{18}$O in dense clumps trace
essentially the same material despite significantly different opacities. We
also found that $J/M$ increases monotonically as a function of $R$ in
power--law form, $J/M~\propto~R^{1.58~\pm~0.11}$. The ratio between rotation
energy and gravitational energy, $\beta$, ranges from 0.0012 to 0.018. The
small values of $\beta$ imply that rotation alone is not sufficient to support
the clump against gravitational collapse.
