Acceleration in an Atwood's Machine

[eagles12]

Homework Statement

An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes over a pulley.
If the pulley is a disk of radius R and mass M, find the acceleration of the masses.
Express your answers in terms of variables m1,m2, M, R, and appropriate constants

Homework Equations

The Attempt at a Solution

I got the equation a=g*m1-m1/m1+m2 but it said this was incorrect because i need to function in M, the mass of the pulley. I am not sure how to incorporate that though.

I also tried a=g*m1-m2/m1+m2+I/r^2
it said this was incorrect also

 

[jambaugh]

You need the moment of inertia of the pulley. For a disk it's 1/2M r^2 .
Note that for a point mass rotating around an axis the MoI is mr^2
A trick then is to treat the pulley as if it were a point mass with the same moment of inertia. You can then ignore the fact it rotates and treat it as an added mass.