Non-tidal variability in ocean currents and bottom pressure is substantial at short periods, but relating the associated signals in ocean angular momentum (OAM) to observed polar motion and length of day fluctuations has been difficult. Our simulations using a barotropic ocean model reveal a clear connection between the estimated OAM signals and both polar motion and length of day at periods of 3--10 days. The dynamic response of the oceans to barometric pressure plays an important role in the excitation of rapid rotation signals. The impact of OAM variability is most clear when using GPS-based Earth orientation measurements with little temporal smoothing. Using the GPS series, and accounting for OAM in addition to atmospheric effects, yields substantial improvements in the excitation budget for rapid polar motion and length of day. The comparisons with Earth rotation data provide a useful check on the rapid ocean variability simulated by the barotropic model.