Left: differential rotation associated with the transient phase of a spin-up induced by mass contraction for E = 10^-6 and Ro = 10^-6 at time τ = 0.02. Dashed (solid) lines represent rotation slower (faster) than the core. Right: profile of the corresponding azimuthal velocity in the equatorial plane as a function of the normalized radius for various times. The curves are scaled by the absolute value of the amplitude at the minimum.