The weak-value-amplification technique has shown great importance in the measurement of tiny physical effects. Here we introduce a polarization-dependent angular velocity measurement system consisting of two Glan prisms and a true zero-order half-wave plate, where a non-Fourier-limited Gaussian pulse acts as the meter. The angular velocities measurements results agree well with theoretical predictions, and its uncertainties are bounded by the Cramér–Rao bound. We also investigate uncertainties of angular velocities for different numbers of detected photons and the smallest reliable postselection probability, which can reach 3.42∗10−6 .