In the conventional treatment of the Earth’s rotational dynamics using the Earth’s angular momentum description (AMD) it is customary to assume that the velocity/displacement of a mass element in the liquid core (LC) has a rigid rotation and a displacement components in addition to the uniform (solid-body) rotation. This makes for a very complex set of differential equations in the treatment of the dynamics of this body. In this work I will use a simple three-layer Earth model with rigid mantle (MT) and inner core (IC) and an incompressible and homogeneous LC to show that it is redundant to assign a rigid rotation component to the motion in the LC. Further, in order to study another shortcoming of the conventional approach above, I will assume that the MT rotates uniformly, and use an approximation commonly used in dealing with the Earth’s rotational dynamics, and find identical analytical results to those in the literature for the periods of the inner-core wobble (ICW) and the free inner-core nutation (FICN). This shows that the aforementioned approximation is not suitable in computing these modes, especially FICN.