A thin circular loop of radius \( R \) rotates about its vertical diameter with an angular frequ...

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A thin circular loop of radius \( R \) rotates about its vertical diameter with an angular frequency \( \omega \). Show that a small bead on the wire loop remains at its lowermost point for \( \omega \leq \sqrt{g / R} \). What is the angle made by the radius vector joining the centre to
\( \mathrm{P} \) the bead with the vertical downward direction for \( \omega=\sqrt{2 g / R} \) ? Neglect friction.

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