We explore spinning , precessing , unequal mass binary black holes to display the long term orbital angular momentum , \vec { L } , flip dynamics . We study two prototypical cases of binaries with mass ratios q = 1 / 7 and q = 1 / 15 and a misaligned spin of the large black hole ( with an intrinsic spin magnitude of S _ { 2 } / m _ { 2 } ^ { 2 } = 0.85 ) . We conduct full numerical simulations , for nearly 14 and 18 orbits respectively , to evolve the binary down to merger and display a full L -flip cycle . The pattern of radiation of such systems is particularly interesting , displaying strong polarization-dependent variation of amplitudes at precessional frequencies , leading to distinctive observational consequences for gravitational wave detectors . These waveform features are strongly directional dependent and measurements of gravitational waves polarizations can be exploited to disentangle the binary ’ s parameters in various astrophysical scenarios .