3
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6d3892e0-8c88-44ec-940f-c526d71a7fc6-2_268_652_1599_475}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6d3892e0-8c88-44ec-940f-c526d71a7fc6-2_191_323_1653_1347}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A small sphere \(S\) of mass \(m \mathrm {~kg}\) is moving inside a smooth hollow bowl whose axis is vertical and whose sloping side is inclined at \(60 ^ { \circ }\) to the horizontal. \(S\) moves with constant speed in a horizontal circle of radius 0.6 m (see Fig. 1). \(S\) is in contact with both the plane base and the sloping side of the bowl (see Fig. 2).
- Given that the magnitudes of the forces exerted on \(S\) by the base and sloping side of the bowl are equal, calculate the speed of \(S\).
- Given instead that \(S\) is on the point of losing contact with one of the surfaces, find the angular speed of \(S\).