Friction of a rolling cylinder I was wondering why friction vectors are drawn differently regarding a cylinder rolling on a surface and a cylinder rolling down an inclined surface. Since friction is responsible for the rotational motion shouldn't it be always pointing in the same direction (given that the cylinder is rotating to the right)?
Here are two pics I googled so you can see what I mean:


 A: 
Since friction is responsible for the rotational motion

That's an assumption. Rotational motion could be caused by something else (like a drive shaft, or an electric motor).
For a rolling object, what friction does is bind together the rotational motion and the lateral motion.
The second case is easier to analyze.  The cylinder is on an incline.  Gravity pulls it down the ramp (linear motion).  Friction creates a torque to cause rotational motion.
The first case is a bit less obvious.  Instead of something forcing the cylinder to move linearly, I assume that something is rotating the cylinder (a torque is being applied in the direction of rotation).  This rotational acceleration is opposed by friction, which pushes the cylinder forward.
So the reason for the opposite directions for friction is that in one case linear motion is driving the rotation, and in the other case rotation is driving the linear motion.  
A: This is because static friction, in the second case, tries to oppose the force which would otherwise result in the movement of the cylinder, which is the component of gravitational force along the inclined plane.
In the second case,  I will assume that the rolling friction has been referred to. Then, the shown direction of friction at that point actually does oppose the direction of rolling at that point, which is the point of contact. 
Edited diagrams to help you understand better: (Sorry for the small text)


A: The first I'm assuming is being rotated or already rotating, so the friction and subsequent torque applied stops it slipping over the surface, and moves instead of just rotating. 
For the second, if there was no friction the object would slide down the surface with no rolling because of gravity, but the friction opposes the way it would move, causing it to rotate.
