# compare the free precession of a disc and a prolate spheroid

For freely rotating rigid bodies, the angular momentum vector ( L ) remains constant, while the angular velocity vector ( $$\omega$$ ) precesses, or wobbles, around it. The rate of this wobble is directly dependent on the object's moment of inertia ratio. For a disc, which has a moment of inertia ratio of 2:1, the precession rate is twice its spin rate. In contrast, for a more elongated object like the spheroid, this ratio is different, leading to a slower precession rate. This illustrates that a body's geometry and mass distribution dictate its complex rotational motion.

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