Spin-up of a turbulent flow in a cylindrical tank caused by a rotating bluff body has been investigated using flow visualization, fluid velocity measurements, and hydrodynamic torque measurements. During the spin-up process three distinct temporal regimes exist. These regimes are: (i) a build-up regime where the torque and the tangential velocity fluctuations in the close proximity of the body remain constant; (ii) a decay regime where these quantities decay with power-law relations; and (iii) a mean flow steady state where these values remain relatively constant. Experiments were conducted in two tanks differing in volume by a factor of 80 and with a large range of bluff body sizes. A non-dimensional time scale, τ, based upon turbulent diffusion is determined and the tangential velocity fluctuations and torque coefficient start to decay at a fixed value of τ. Likewise, steady state is attained at a larger fixed value of τ. This time scaling is physically based upon the time required for momentum to be transferred over the entire tank volume due to turbulent diffusion, and is general for any body size, tank size, rotation rate, and acceleration rate.