Vertical transport of horizontal momentum due to baroclinic instabilities is investigated in a rotating stratified fluid. The experiments were carried out in the large rotating tank of the Coriolis-LEGI laboratory in Grenoble with flat bottom and linear density stratification. The mean flow was generated by increasing (spin up) or decreasing (spin down) the rotation rate of the platform. The velocity fields were measured by PIV (Particle Image Velocimetry) technique. The dimensionless parameters that are important in determining the observed response are the Burger number and the Rossby number. Our experimental study reveals two very different behaviors. For O(1) Burger numbers, the bulk of the flow remains axisymmetric with a very slow decay. We have checked that the decay is well described by the usual vertical diffusion law, except in a region near the boundaries. The mismatch pertains to the presence of Ekman pumping/suction, but this mechanism is confined by stratification to a relatively shallow layer. For Burger numbers ≪ O(1), baroclinic instabilities are observed. The increased vertical momentum transport leads to a much faster spin than the previous case. Neither the diffusion nor the Ekman pumping/suction can be considered responsible for this enhanced transport of momentum and we interpret it as the effect of baroclinic instabilities. Eady's theory is used to analyse the quasi-geostrophic baroclinic stability problem and a model is proposed to estimate the azimuthal velocity decay. The results are presented and discussed.