Physics Lab Help - Moment of inertia and acceleration

[NinjaChachi]

Homework Statement

In our physics lab we were to set up a system looking like this:

where the mass was released and the velocity/acceleration and of the ring was calculated using MotionLab software. Our goal was to find the predicted total moment of inertia by just calculating the moment of inertia of the ring, disk, and axle and comparing it to the actual using the acceleration we get. It was very easy to calculate the total inertia but I am having trouble interpreting the graphs motionlab gave us and relating that to the total moment of inertia.
I will attach the graphs we obtained in one trial (keep in mind the line of best fit is not fully accurate as we were short on time)

Homework Equations

I think we use the following equation to relate acceleration of the system to total moment of inertia
I=r^2/a * m(g-a)
and I already found all the individual moments of inertia which was not a problem

The Attempt at a Solution

I tried plugging in 13.8 from the Vx/time equation into my above equation and did not get remotely close to the same moment of inertia. What do I actually use as my acceleration? Also, is that total moment of inertia equation correct?

Thanks

 

[haruspex]

What is x, in relation to the set-up?
Why would it oscillate? There's no obvious reason for oscillations in the diagram. Is it to do with how the string is attached to the spool? What is the meant by '3 stage spool'?
In your predicted equations, position comes out as constant 1, while velocity comes out as constant zero. Are all the constants becoming zero because there are not enough digits shown?

 

[NinjaChachi]

What is x, in relation to the set-up?
Why would it oscillate? There's no obvious reason for oscillations in the diagram. Is it to do with how the string is attached to the spool? What is the meant by '3 stage spool'?
In your predicted equations, position comes out as constant 1, while velocity comes out as constant zero. Are all the constants becoming zero because there are not enough digits shown?

x is simply the position. We took a video looking down on the disk. Disregard the '3 stage spool' we didn't have the string wrapped around that. just around the axle. We didn't truly predict these lines of best fit either. More of a guess than anything. I just really don't know how to get acceleration out of these graphs/formulas.

 

[haruspex]

x is simply the position. We took a video looking down on the disk. Disregard the '3 stage spool' we didn't have the string wrapped around that. just around the axle. We didn't truly predict these lines of best fit either. More of a guess than anything. I just really don't know how to get acceleration out of these graphs/formulas.

Yes, but position of what? Ok, I think I've figured it out... it's the x-coordinate of some point on the disk, right? Hence the oscillation.
So you need equations which predict the position and velocity on the assumption of constant angular acceleration and a moment of inertia I. Your equations are of the right form, but don't reference I. Presumably you know the weight of the descending mass and radius of the axle.

Why did you not use the spool? How was the string wrapped around the axle, exactly? Did the later turns wrap over the early turns, effectively increasing the radius, or were you careful to ensure that all turns contacted the axle directly?