K&K Question 3.22 – Mass, String, and Ring

1. The problem statement, all variables and given/known data

A mass m whirls around on a string which passes through a ring, as shown. Neglect gravity. Initially the mass is distance r0 from the center and is revolving at angular velocity ω0. The string is pulled with constant velocity V starting at t = 0 so that the radial distance to the mass decreases. Draw a force diagram and obtain a differential equation for ω. This equation is quite simple and can be solved either by inspection or by formal integration.

2. Relevant equations

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3. The attempt at a solution

I have absolutely no idea on how to start this problem. I cannot obtain a valid differential equation from the tension, and I do not know how to relate the normal force to everything. Even if I write:
It is still impossible to get a valid differential equation. I don’t even think the relation [itex]\theta=s/r[/itex] would help.


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