  To answer a question of how can one observed angular momentum radiation near
null infinity, one can first transform the dynamical twisting vacuum solution
and make it satisfy Bondi coordinate conditions in the asymptotical region of
the null infinity. We then obtain the Bondi-Sachs news function and also find
the relationship of how does the angular momentum contribute to the news
functions from the exact solution sense. By using the Komar's integral of
angular momentum, the gravitational angular momentum flux of the dynamical
twisting space-time can be obtained. All of our results can be compared with
the Kerr solution, Robbinson-Trautmann or Schwarzschild solution. This study
can provide a theoretical basis to understand the correlations of gravitational
radiations near a rotating dynamical horizon and null infinity.
