Help Deriving formula for moment of inertia lab

AI Thread Summary
The discussion revolves around deriving the formula for the moment of inertia in a lab setting. The initial attempt resulted in an incomplete formula, I=mgb/al - mb^2, with confusion over the correct application of angular acceleration. The user shared their calculations involving net force and torque but struggled to reach the correct solution. Ultimately, they realized that substituting linear acceleration with angular acceleration multiplied by the radius clarified their approach, leading to the correct answer. The user expressed gratitude for any assistance received during their problem-solving process.
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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 :)
 
Last edited:
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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
 
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