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So I'm looking at a problem that involves a situation that looks like this

the cylinder rolls without gliding.

And there are these following equations that apply to it

(1) mg - T = ma (for the block hanging vertically)

(2) T + f = Ma (for the cylinder f = friction force, T = String force)

(3) Tr - fr = Ia (I = inertia, r = radius)

I'm only concerned about equation (2) where it's T + f = Ma, shouldn't it be T - f = Ma? Because the tension from the string and friction force are opposite to eachother. It is apparantly acknowledged that they are opposite in equation (3) where the torques are opposite, but why not in equation (2)?

the cylinder rolls without gliding.

And there are these following equations that apply to it

(1) mg - T = ma (for the block hanging vertically)

(2) T + f = Ma (for the cylinder f = friction force, T = String force)

(3) Tr - fr = Ia (I = inertia, r = radius)

I'm only concerned about equation (2) where it's T + f = Ma, shouldn't it be T - f = Ma? Because the tension from the string and friction force are opposite to eachother. It is apparantly acknowledged that they are opposite in equation (3) where the torques are opposite, but why not in equation (2)?