We begin by considering a rotating Boussinesq fluid in a box with stress-free walls. Because the velocity field of a Boussinesq fluid is solenoidal, it is helpful to employ a poloidal-toroidal (PT) representation. However, upon careful analysis in the PT frame work, a problem is reveled. Coriolis accelerations do not conserve energy! At first, one might think the problem is with the PT formalism and not with Coriolis accelerations. When one switches to the full primitive equations, kinetic energy is properly accounted for. However, the misery is merely pushed around and the problem has not gone away. Indeed, rotation causes the pressure equation to be ill-posed! It is clear that there is something wrong when rotating systems and stress-free boundaries are naively combined. Nevertheless, we would not like to banish stress-free boundaries since they are so easy to work with numerically. We will see that there is a way to fix the above problems through the formulation of weak equations. In doing this, we will gain some insight into the physics of a type of motion that has been observed in laboratory experiments; precessing waves.