# Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems impossible to me. Assuming that the axis of symmetry of the top is the $z$-axis, how can $\overrightarrow \omega$ point in any direction other than the $z$-axis? It's got to rotate about the $z$-axis and hence point along it. What am I missing?

• The general derivation is done on the assumption that the symmetry axis of the top is not vertical. It is, however, interesting to ask what happens when it is. – dmckee Sep 20 '12 at 4:25
• @Joebevo (possibly off topic): no reason for typesetting physics to be a pain, which it will be if you have to type \overrightarrow all the time. Try \vec{x} instead. It also formats better :) – user10851 Sep 20 '12 at 5:53