Another rotation problem -- Acceleration of a ring rolling on a surface

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The discussion centers on a physics problem involving a rotating ring on a surface, specifically analyzing the acceleration of the center, the frictional force from the ground, and the normal reaction when the ring's geometric center has a velocity of $$ \sqrt{gR} $$. Participants are encouraged to provide their attempts at solving the problem to facilitate guidance. The conversation emphasizes the importance of showing work to receive constructive feedback. The thread also references a related discussion for additional context.
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[Mentors' note - this question was spun off from https://www.physicsforums.com/threa...urface-but-with-a-twist.1078618/#post-7243282 which contains the homework template information]

I'm not sure if I can add on by adding a similar question, if I am not allowed someone please tell me.

A ring is rotating as shown in the figure. At that particular instant when the velocity of the geometric center is $$ \sqrt{gR} $$ find the
1. Acceleration of center
2. Frictional force from ground
3. Normal reaction
 

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palaphys said:
[Mentors' note - this question was spun off from https://www.physicsforums.com/threa...urface-but-with-a-twist.1078618/#post-7243282 which contains the homework template information]

I'm not sure if I can add on by adding a similar question, if I am not allowed someone please tell me.

A ring is rotating as shown in the figure. At that particular instant when the velocity of the geometric center is $$ \sqrt{gR} $$ find the
1. Acceleration of center
2. Frictional force from ground
3. Normal reaction
Where is your attempt?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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