The accessibility of a system is a necessary condition for its controllability. This property is linked to the rank of the Lie algebra generated by the drift and input vector fields. In case of polynomial dynamical systems the Lie subalgebra can be computed using methods of algebraic geometry. An interesting system falling into this class is the rotation of a rigid body, in particular its angular momentum. We attempt to decide the accessibility of this system in dependence of the inertia parameters for simple cases.