A thin circular loop of radius R rotates about its vertical diameter with an angular frequency w. Show that a small bead on the wire loop remains at its lowermost point for ω ≤ √ (g / R) . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω = √(2g / R )? 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 w. Show that a small bead on the wire loop remains at its lowermost point for ω ≤ √ (g / R) . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω = √(2g / R )? Neglect friction.
Answer» A thin circular loop of radius R rotates about its vertical diameter with an angular frequency w. Show that a small bead on the wire loop remains at its lowermost point for ω ≤ √ (g / R) . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω = √(2g / R )? Neglect friction.

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