We have developed an evaporative cooling technique that accelerates the circulation of an ultra-cold $^{87}$Rb gas, confined in a static harmonic potential. As a normal gas is evaporatively spun up and cooled below quantum degeneracy, it is found to nucleate vorticity in a Bose-Einstein condensate. Measurements of the condensates aspect ratio and surface-wave excitations are consistent with effective rigid-body rotation. Rotation rates of up to 94% of the centrifugal limit are inferred. A threshold in the normal clouds rotation is observed for the intrinsic nucleation of the first vortex. The threshold value lies below the prediction for a nucleation mechanism involving the excitation of surface-waves of the ground-state condensate.
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