How do I properly set up this F.B.D.?

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To set up the free body diagram (F.B.D.) for a uniform solid cylinder rolling down an incline, it is essential to focus on static friction since the cylinder rolls without slipping. The equation mgsin(theta) - μs = ma should be used, where μs represents the static friction coefficient. The discussion emphasizes that two equations should be established: one for translational motion and another for rotational motion, incorporating static friction. The proper approach is to analyze the forces and torques acting on the cylinder to find the acceleration of its center of mass. Understanding the role of static friction is crucial for accurately solving the problem.
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Homework Statement


A uniform solid cylinder of wood rolls without slipping down an incline of angle theta. the coefficient of static friction is μs and kinetic friction is μk. Find the acceleration of the center of mass of the cylinder.

Homework Equations


mgsin(theta)-μk = ma

The Attempt at a Solution


My question is really how to reconcile with the static friction coefficient. Should this be included in my FBD and so my equation? Or would I just be using the μk and not the μs? If μs is to be included, can you please explain how? Would I have to set up two equations, one to overcome the static friction and the other to characterize the rolling motion with μk, then solve for the acceleration using a two-equation system?
 
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You are told that the cylinder rolls without slipping, thus the only friction involved is static friction. (Hint: Write two equations: one for rotation, one for translation.)
 
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