Double-modulated terahertz differential time-domain spectroscopy (double-modulated THz-DTDS), is a technique that is based on dithering the sample under test. In this paper, we report a measurement technique based on mounting the sample on a spinning wheel, in order to overcome fundamental limitations imposed by linear dithering. We demonstrate a proof-of-principle showing that noise decreases as a function of the spinning wheel modulation frequency. This technique does not suffer the mechanical noise limitation of traditional linear dithering and thus opens up future scope for further noise reduction via hardware advances in the modulation frequency of the wheel. The spinning wheel technique enables a rapid succession of measurements between the reference and sample signals with a single mechanical delay scan. As a result, an improvement in measurement time by at least a factor of two, as compared to the conventional THz-TDS measurement technique is observed. The spinning wheel technique is experimentally verified by measuring the dielectric properties of a thick polymer material.