All Problems Dynamics of a solid body
Problem 1.285
A top of mass \(m=1.0 \mathrm{~kg}\) and moment of inertia relative to its own axis \(I=4.0 \mathrm{~g} \cdot \mathrm{m}^{2}\) \(\begin{array}{lllll}\text { spins } & \text { with } & \text { an } & \text { angular } & \text { velocity } & \omega\end{array}\) \(=310 \mathrm{rad} / \mathrm{s} .\) Its point of rest is located on a block which is shifted in a horizontal direction with a constant acceleration \(w=1.0 \mathrm{~m} / \mathrm{s}^{2}\). The distance between the point of rest and the centre of inertia of the top equals \(l=10 \mathrm{~cm}\). Find the magnitude and direction of the angular velocity of precession \(\omega^{\prime}\).
\[ \text { 1.285. } \quad \omega^{\prime}=m l \sqrt{g^{2}+w^{2}} / I \omega= \] \(=0.8 \mathrm{rad} / \mathrm{s} .\) The vector \(\omega^{\prime}\) forms the angle \(\theta=\arctan (w / g)=6^{\circ}\) with the vertical.