# Homework Help: Find the aceleration of the disk when falling (rotation)

1. Jun 29, 2012

### Hernaner28

1. The problem statement, all variables and given/known data

I have that system and the problem says:

A disk of mass M and radious R are posed are shown. The disk is hanging by an ideal rope which is coiled up. From a smooth axis through the center of the disk is haning a body m. Calclate the module of the aceleration of the center of mass of the disk.

2. Relevant equations

3. The attempt at a solution

I've done this excercise but without the small mass hanging there. What I did was to use the torque and newton formulas, that simple. But here I've got two bodies and tensions are driving me crazy. Should I consider the bodies as a single one?

Thanks!

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2. Jun 29, 2012

### tiny-tim

Hi Hernaner28!
Yes, since they're moving together, you can regard them as a single body …

add the m to the mass of the pulley, but not to its moment of inertia.

3. Jun 29, 2012

### Hernaner28

Done! Thank you!!

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4. Jun 29, 2012

### tiny-tim

yes!

here's a shortcut (i don't know whether your professor would approve of this, but it's certainly a good way of checking the answer) …

the force is (M+m)g, and the effective mass is the actual mass M+m plus the "rolling mass" I/r2 = M/2,

so a = (M + m)/(3M/2 + m)