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

Image: http://ift.tt/1gcjfPX
$$r=Vdt$$
$$\frac{V^2}{r}=Vd\omega$$
$$T=\frac{mV^2}{r}=mr\omega^2=mV^2dtd\omega$$
$$N=m\ddot{y}$$

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:
$$\frac{dv}{dt}=V^2dtd\omega$$
It is still impossible to get a valid differential equation. I don’t even think the relation $\theta=s/r$ would help.

http://ift.tt/1gPbETl