Find the Angular Acceleration with and Without the disk inertia

[Northbysouth]

Homework Statement

Determine the angular acceleration of the uniform disk if (a) the rotational inertia of the disk is ignored and (b) the inertia of the disk is considered. The system is released from rest, the cord does not slip on the disk, and bearing friction at O may be neglected. The angular acceleration is positive if counterclockwise, negative if clockwise.

I have attached an image of the question

Homework Equations

The Attempt at a Solution

m1 = 1.5 kg
m2 = 3.1kg
r = 0.32m

I started by summing the moments about O

ƩM_O = (-m1gr + m2gr)/I_O

I_O = 2mr² but I'm not sure why this is the case. A classmate of mine said something about adding in the inertias from the weight but I'm not sure what this means.

Also, how to I account for the disk inertia?

Any advice would be appreciated.

 

[Simon Bridge]

I started by summing the moments about O

... which confused you.

The force on the disk comes from the tensions acting at opposite points.
The tensions come from the weights. The equation is ƩM = Iα ... which is not the same as:

ƩM_O = (-m1gr + m2gr)/I_O

Breaking it down:

In the first case you would be better to find the linear acceleration of the weights, and use that to deduce the angular acceleration of the disk.

In the second case, you have three free-body diagrams instead of just two.
You need ƩF=ma as well as ƩM = Iα