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.
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