We analyze the random disturbance in the transmission of light through a spinning Glan-Thompsontype prism polarizer. The disturbance makes the dependence of the transmission on the rotation angle significantly deviates from the Malus cosine-squared law and severely spoils the output light quality. Slight vibration of the polarizer as it rotates combing the multi-beam-interference effect raises the disturbance. Further analysis reveals the sensitive dependence of the disturbance on the composing material of the prism gap, and the appropriate selection of such material can make the disturbance minimize to very desirable levels. The model results show quite good agreement with experiments.