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

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In summary, the problem involves a solid cylinder rolling down an incline with an angle theta. The coefficient of static friction is μs and the coefficient of kinetic friction is μk. The acceleration of the center of mass of the cylinder can be found by writing two equations, one for rotation and one for translation, and solving for the acceleration using a two-equation system. The only friction involved is static friction since the cylinder is rolling without slipping.
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Vitani11
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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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Related to How do I properly set up this F.B.D.?

1. How do I determine the direction of the force in a free body diagram?

The direction of the force should be drawn in the direction that the object is being pushed or pulled. If there are multiple forces acting on the object, they should be drawn in the appropriate directions based on their magnitude and direction.

2. What are the different types of forces that should be included in a free body diagram?

The most common types of forces that should be included in a free body diagram are gravitational forces, normal forces, frictional forces, and applied forces. Other types of forces may also need to be included depending on the specific situation.

3. How do I determine the magnitude of the forces in a free body diagram?

The magnitude of the forces should be determined based on the size and strength of the force. This can be done by using measurements or calculations based on known values such as mass and acceleration.

4. What are some common mistakes to avoid when setting up a free body diagram?

Some common mistakes to avoid when setting up a free body diagram include not including all relevant forces, drawing forces in the wrong direction, and not labeling the forces with the correct units. It is also important to make sure that the diagram is neat and organized to avoid confusion.

5. Why is it important to properly set up a free body diagram?

A properly set up free body diagram is important because it helps to visually represent all the forces acting on an object, making it easier to analyze and understand the motion of the object. It also allows for more accurate calculations and predictions of the object's behavior.

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