Consider a rigid body of spheroidal shape, which can be oblate (c a, e.g. a rugby ball, see the right figure). It is initially rapidly spinning about its axis of symmetry. We assume that the axis of symmetry is tilted so that it is not vertical to the surface of the Earth. Now we place it on a smooth (frictionless) flat table. Show that the directions of the precession of the axis for the two cases are opposite to each other. Also, show that for a perfect sphere (a = c) it never precesses.

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