Observations of the winds in tropical cyclones are still limited. We propose a new method for deriving the tangential winds in tropical cyclones, which employs a spectral analysis of high-frequency cloud imaging by latest-generation geostationary meteorological satellites such as Himawari-8. The method was applied to the visible images of boundary layer clouds in the eye of Typhoon Lan (2017) over an 8.5-hour period. The low-level tangential winds over the central two-thirds of the eye in radius were close to a rigid body rotation and increased with time. On its outside was a region with striating clouds rotating at much higher angular velocities, which may have been super-gradient. Asymmetric motions were visualized as the deviation from the inner rotation, and the vorticity of some mesovortices were quantified. These asymmetric motions are suggested to transport angular momentum to accelerate the inner rotation.