# 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?

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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 :) –  Chris White Sep 20 '12 at 5:53

Think of a single particle, an electron, moving in the x y plane and a magnetic field perpendicular to its direction of motion, the z direction.

The electron will trace a circle, the angular velocity is associated with the electron and not the z axis passing through the center of its circle. Just the z direction. As the electron could be described as precessing so one could describe the omega associated with it as precessing . I agree it is a confusing terminology for a rigid body.

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