A ring of mass \( m \) and radius \( R / 4 \) rolls inside a fixed hoop of radius \( R \) such t...

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A ring of mass \( m \) and radius \( R / 4 \) rolls inside a fixed hoop of radius \( R \) such that at the highest point of its trajectory the normal reaction becomes zero. The friction on the hoop is sufficient to ensure pure rolling. Find the angular velocity of the ring in \( \mathrm{rad} / \mathrm{s} \). (Given \( R=0.3 \mathrm{~m} \) and \( g=10 \mathrm{~m} / \mathrm{s}^{2} \) )
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