# Angular momentum thin string problem

1. Oct 17, 2005

### aquafina

A thin string is wrapped around a cylindrical hoop of radius R and mass M. One end of the string is fixed and the hoop is allowed to fall vertically starting from rest, as the string unwinds. a)Determine the angular momentum of the hoop about its CM as a function of time. b)What is the tension in the string as a function of time.

I'm having a hard time even picturing this and how the hoop would rotate as the string unwinded. Some hints would be really helpful, thanks.

2. Oct 17, 2005

### andrevdh

Does this help a bit?

Last edited: Nov 29, 2006
3. Oct 17, 2005

### lawtonfogle

Im not sure about A (just starting this in my class), but it seems logical that the object is in free fall, so would their even be a tension?. But then again, it would take a force to make the string unwind..

4. Oct 18, 2005

### andrevdh

If you investigate my suggestion you will find that the tension has an x-component which cannot be cancelled by any other force. This means that the hoop moves untill the tension has no x-component! The hoop is therefore pushed sideways by the tension until the point where the string leaves the hoop is underneath the point where the string is held.Taking the moment of the tension around the com gives:
\begin{align*} TR=I\alpha\\ =I\frac{d\omega}{dt}\\ TRdt=Id\omega\\ TR\int_{0}^{t}dt=I\int_{0}^{\omega}d\omega\\ ... \end{align*}

Last edited: Nov 29, 2006