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**on the acceleration of a cylinder down a ramp**

This problem has been vexing me for some time, for the life of me I can't figure it out or figure out why I can't figure it out. It seems like gsin(Θ)=a+αr, where Θ is the angle of the ramp, a is the acceleration, α is the angular acceleration, and r is the radius of the cylinder. Which would tell me that a=gsin(Θ)/2 and α=gsin(Θ)/(2r). But then another train of thought leads me to think that a=gsin(Θ) and that α=gsin(Θ)/r, which would mean a+αr=2gsin(Θ). So the question is, given Θ, r, and maybe m if neccesary, how do you find a and α?

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