The angular acceleration of a spinning object can be estimated by probing the object with Laguerre-Gauss (LG) beams and analyzing the rotational Doppler frequency shift of returned signals. The frequency shift is time dependent because of the change of the rotational angular velocity over time. The detection system is built to collect the beating signals of LG beams back-scattered from a non-uniform spinning body. Then a time-frequency analysis method is proposed to study the evolution of the angular velocity in time. The experimental results of different angular accelerations of the rotator are consistent with expectations. The measurement errors of different probe beams with various topological charges from l = ± 10 to l = ± 100 are also investigated.