Deriving moment of inertia from rotational dynamics

[HT3]

this lab is very similar to mine
basically i can only seem to derive a portion of the formula, I=mgb/al - mb^2
where b- radius, g-gravity, al- angular acceleration.
I do not get the right answer:
here is what i did do however,
Fnet=ma
T-mg=-ma (acceleration is downwards)
so T=(mg-ma)
so then

Tnet=I*al (where al is angular acceleration not acceleration)

so then
T*b=I*al
(b*mg-b*ma)/al = I

as u can see this is not the correct solution..but is a start
the solution i need to get to is
I=mgb/al - mb^2
can someone help me out - thanks :)

 

[HT3]

NEVERMIND I SOLVED IT i was on the right way i just realized that a=al*R and if i plug that in my answer is correct.
thanks to any1 who viewed it anyways