Stimulated by considerations of the shear structure of the tropospheric jet stream, we have performed a series of experiments in a rotating vessel (using water, barotropic model) to study the angular momentum exchange in a rotating fluid. In the experiments, a cylinder was fitted in the centre of a cylindrical vessel (of large diameter) rotating around the vertical axis and could rotate independently around the same axis in both directions. The experimental results are as follows. (i) For constant relative rotation with the inner cylinder acting as a source (sink) of angular momentum, the momentum exchange becomes stationary, the bottom of the vessel being a sink (source) of momentum. The zone for this exchange is confined to a relatively small area around the inner cylinder. Beyond this zone, the ‘friction’ zone, no relative motion can be observed. Essentially the radial extent b of the ‘friction’ zone depends on the dimensionless parameter ε = Δω/ω (Δω = relative rotation rate of inner cylinder, ω = rotation rate of vessel): b(|ε|) > b(–|ε|). (ii) The velocity field shows a strong tendency to be two-dimensional, the radial and vertical components being about one to two orders of magnitude smaller than the zonal component, whose absolute value decreases monotonically from the inner cylinder to the outer limit of the ‘friction’ zone. Elementary analytical considerations indicate that inertial stability seems to be the key for the understanding of these results.