Ring on a rotating shaft!

An oiled horizontal cylindrical shaft rotates around its own axis at a constant speed. A ring with the inner diameter twice the diameter of the shaft is placed on the shaft. Depending on the tilt of the ring, it can travel along the shaft in either direction. What is the quantitative relationship between relevant angles and the velocity or acceleration of the ring along the shaft? Here we assume that the friction coefficient between the ring and the shaft is constant.

#Mechanics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$