The top shown is supported at the fixed point O and its moments of inertia about its axis of symmetry and about a transverse axis through O are denoted, respectively, by I and I??.

(a) Show that the condition for steady precession of the top is (Iωz ?? I?? φ cos θ) φ = WC where φ is the rate of precession and z ω is the rectangular component of the angular velocity along the axis of symmetry of the top.

(b) Show that if the rate of spin ψ of the top is very large compared with its rate of precession φ, the condition for steady precession is I ψφ ?? Wc.

(c) Determine the percentage error introduced when this last relation is used to approximate the slower of the two rates of precession obtained for the top of Prob. 18.105.

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