It is known that, in a linear shear flow, fluid inertia causes a particle to spin more slowly than the surrounding fluid. The present experiments performed with a sphere with fixed centre, but free to rotate in a fluid undergoing solid-body rotation around a horizontal axis indicate that the spin rate of the sphere can be larger than that of the flow when the sphere is sufficiently far from the axis. Numerical simulations at Reynolds number 5≤Re≤200 confirm this observation. To gain a better understanding of the phenomenon, the rotating flow is decomposed into two shear flows along orthogonal directions. It is found numerically that the cross-stream shear has a much stronger effect on the particle spin rate than the streamwise shear. The region of low stress at the back of the sphere is affected by the shear component of the incident flow. While for the streamwise case the shift is minor, it is significant for cross-stream shear. The results are interpreted on the basis of the effect of the shear flow components on the quasi-toroidal vortex attached in the sphere's near wake. The contributions of streamwise and cross-stream shear to the particle spin can be linearly superposed for Re=20 and 50.