Fluid dynamics | Torque on rotating sphere

In this video we will derive the expression for the torque on a slowly rotating sphere in a newtonian fluid. Namely M=-8πa³ηω. (There is a mistake at the beggining of the video, the numerical factor is not 8/3) This relation is used for calculating the viscosity by the Electromagnetically Spinning Viscometer, which was first deviced by Sakai et al. at the Tokyo University. Derivation of the flow: https://www3.nd.edu/~mjm/rotatingsphere.pdf Also see (cartesian derivation) https://www.youtube.com/watch?v=dyx_nAi1YXw