We study the su(2) conformal field theory in its spinon description, adapted to the yangian invariance. By evaluating the action of the yangian generators on the primary fields, we find a new connection between this conformal field theory and the Calogero-Sutherland model with su(2) spin. We use this connection to describe how the spinons are the quasi-particles spanning the irreducible yangian multiplet, and also to exhibit operators creating the N-spinon highest-weight vectors.