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 $\omega^{\prime}$.