The math help thread

Ooh, ooh. I think I got the acceleration derivation for the third problem. :]

F[SIZE="1"]N[/SIZE] - f[SIZE="1"]k[/SIZE] = ma --> mgsinθ - f[SIZE="1"]k[/SIZE] = a --> gsinθ - f[SIZE="1"]k[/SIZE]/m = a
T = Iα = rf[SIZE="1"]k[/SIZE] ---> Iα/r = f[SIZE="1"]k[/SIZE]
rα=a --> α=a/r

Substitute for f[SIZE="1"]k[/SIZE]:

gsinθ - Iα/mr = a
gsinθ - mr^2α/2mr = a
gsinθ - mr^2a/2mr^2 = a
gsinθ - a/2 = a
gsinθ = 3/2a
a = 2/3*gsinθ

Can anyone confirm this?