OK pulled the book out and I think we're both right - kinda:
You've modeled the wheel as a thin shell therfore I=mr^2
I modeled it as a thin disc with so ariving at I=mr^2/2
Where what may be more appropriate but overcomplicating things for the purpose of proving (or disproving as the case may...
Think we're disagreeing on value for Inertia of a wheel, from memory I though mass moment of inertia of a solid disc about it's origin was m*r^2/2, memory could be failing ;-)have to check that...?
Rgds
Sean
I didn't quite follow as to how the figure of 2:1 was arrived at so had a go at the Energy method and came up with a slightly different result:
The change in kinetic energy of the system due to a change in wheel mass "m" at radius "r" on a wheel with a radius of...