Conservation of Angular Momentum

[murphy]

I have a physics problem that I think is not so hard but I just can't get the answer. There are two uniform circular disks that are rotating and attached by a string. there is no slip between the string and the disks. On the small disk is a hub that is attached like the first two to an even smaller disk by string. The radii are given for the three disks and the hub, and the smallest disk and largest disk have equal densities and thickness. I am asked to find the ratio between the magnitude of the angular momentum of the biggest disk to the angular momentum of the smallest disk. All the disks are spinning in the same direction. I added a picture of this but I'm not sure how exactly so it might not show. I appresciate any help I can get with this!

 

[Tide]

I get

$$\frac {L_C}{L_B} = \frac {R_A R_C}{R_B^2}$$

on my first runthrough.

 

[Doc Al]

The angular momentum of each disk is $L = I \omega$. Disks connected by strings will have the same tangential speed ($v = \omega R$); use that fact to relate the angular speeds of the connected disks.

My answer differs from Tide's. ($L_C/L_B$ will depend on the hub radius, for one thing.) But I think you can figure it out for yourself. (Why should Tide and I have all the fun? )

 

[Tide]

Al,

You're right - I mistyped my expression off my notepad but we'll let Murphy figure it out! :-)

 

[murphy]

Thanks! I love this forum!