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Homework Statement
A mass ##m## whirls around on a string which passes through a ring. Neglect gravity. Initially the mass is at distance ##r_0## from the center and is revolving at angular velocity ##\omega _0##. 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 ##\omega##
Homework Equations
The Attempt at a Solution
So, the force diagram has only one force, which is the tension on the string acting on the mass. Because the string is shortening by ##v = \dot{r}##, I set up the equation ##T = F_r = m(-r\omega ^2 +r\omega +2v\omega)##
If we divide out ##m## we get ##\mathbf a = -r\omega ^2 +r\omega +2v\omega##, I'm not exactly sure what we're suppose to get on the other side.
I'm asking for a hint, or maybe a word of advice. The book says the answer should be simple and easy to integrate.