We classify the simple modules for the rational Cherednik algebra $\bf{H_{0,c}}$ that are irreducible when restricted to $W$, in the case when $W$ is a finite Weyl group. The classification turns out to be closely related to the cuspidal two-sided cells in the sense of Lusztig. We compute the Dirac cohomology of these modules and use the tools of Dirac theory to find nontrivial relations between the cuspidal Calogero-Moser cells, in the sense of Bellamy, and the cuspidal two-sided cells.