A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for ω≤√gr. What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω=√gr? Neglect friction.

A thin circular loop of radius R rotates about its vertical diameter w

1.	A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for ω≤√gr. What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω=√gr? Neglect friction.
Answer» A thin circular loop of radius R rotates about its vertical diameter with an angular frequency $ω$ . Show that a small bead on the wire loop remains at its lowermost point for $ω \leq \sqrt{\frac{g}{r}}$ . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for $ω = \sqrt{\frac{g}{r}}$ ? Neglect friction.

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