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.