How to Account for Rotational Motion in a Pulley Problem?

[danny271828]

A massless string is placed over a massless pulley, and each end is wound around and fastened to a vertical hoop. The hoops have masses M1 and M2 and radii R1 and R2. The apparatus is placed in a uniform gravitation field g and released with each end of the string aligned along the field.



I have to show that the tension is t = gM1M2/(M1+M2)



I keep getting twice this value.

 

[Astronuc]

Please show one's work.

This is a variation on Atwood's machine -
http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html

- which is made a little more complicated by the fact that the masses have different moment arms.

 

[Gravitino]

I keep getting twice this value.

You are getting twice of the value, because you are neglecting the rotational motion of the hoops. The answer you got (twice value) is in the case when hoops are pointlike.