A round cone with half-angle \( \alpha=30^{\circ} \) and the radius of the base \( R=5.0 \mathrm...

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A round cone with half-angle \( \alpha=30^{\circ} \) and the radius of the base \( R=5.0 \mathrm{~cm} \) rolls uniformly and without slipping over a horizontal plane as shown in Fig. 1.8. The cone apex is hinged at the point \( O \) which is on the same level with the point \( C \),
Fig. \( 1.8 \) the cone base centre. The velocity of point \( C \) is \( V=10.0 \mathrm{cms}^{-1} \). Find the moduli of the vector of the angular velocity of the cone and the angle it forms with the vertical
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