We present high-angular-resolution ALMA (Atacama Large Millimeter Array) images of N$_{2}$H$^{+}$ (1--0) that has been combined with those from the Nobeyama telescope toward OMC-2 and OMC-3 filamentary regions. The filaments (with typical widths of $sim$ 0.1 pc) and dense cores are resolved. The measured 2D velocity gradients of cores are between 1.3 and 16.7 km,s$^{-1}$,pc$^{-1}$, corresponding to a specific angular momentum ($J/M$) between 0.0012 and 0.016 pc,km,s$^{-1}$. With respect to the core size $R$, the specific angular momentum follows a power law $J/M propto R^{1.52~pm~0.14}$. The ratio ($beta$) between the rotational energy and gravitational energy ranges from 0.00041 to 0.094, indicating insignificant support from rotation against gravitational collapse. We further focus on the alignment between the cores rotational axes, which is defined to be perpendicular to the direction of the velocity gradient ($theta_{G}$), and the direction of elongation of filaments ($theta_{f}$) in this massive star-forming region. The distribution of the angle between $theta_{f}$ and $theta_{G}$ was f ound to be random, i.e. the cores rotational axes have no discernible correlation with the elongation of their hosting filament. This implies that, in terms of angular momentum, the cores have evolved to be dynamically independent from their natal filaments.
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