Problem 1.283

A top of mass $m=0.50 \mathrm{~kg}$, whose axis is tilted by an angle $\theta=30^{\circ}$ to the vertical, precesses due to gravity. The moment of inertia of the top relative to its symmetry axis is equal to $I$ $=2.0 \mathrm{~g} \cdot \mathrm{m}^{2}$, the angular velocity of rotation about that axis is equal to $\omega=350 \mathrm{rad} / \mathrm{s},$ the distance from 'the point of rest to the centre of inertia of the top is $l=10 \mathrm{~cm} .$ Find: (a) the angular velocity of the top's precession; (b) the magnitude and direction of the horizontal component of the reaction force acting on the top at the point of rest.