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Dynamics of rigid bodies rotating about an arbitrary fixed axis

The definitions of the angular momentum and torque about a fixed point are used to derive the equation of motion of a rigid body rotating about an arbitrary fixed axis. It is shown that the angular momentum (torque) and angular velocity (acceleration) vectors are parallel to each other if the fixed reference point is chosen as follows: (i) for a body of arbitrary shape rotating about a principal axis, to be at the origin of the principal axis coordinate system, which need not be the centre of mass of the rigid body; (ii) for a body rotating about an axis of symmetry, to be anywhere on the axis of rotation; (iii) for a body rotating about an axis perpendicular to the plane of symmetry, to be at the intersection of the axis of rotation with the symmetry plane. The method described is particularly useful as its leads in a natural way to the special case of rigid body rotation about an arbitrary fixed axis.