Friction force in rotating and translating objects?

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I need a better understanding of how to think of or view the friction force vector in a rotating and translating object....

I know the friction force vector for a translating object is opposite the direction of travel. If the object, say a sphere, is also rotating around an axis that is perpendicular to the direction of translating motion then the friction force vector remains opposite the direction of travel. What if the axis of rotation is rotated in the horizontal plane, say 45 degrees, from the direction of travel. What is the direction of the friction force vector? Would there be a friction vector for the translational motion and one for the rotational motion so their vector sum would define the overall friction vector?

I would appreciate any comments on this matter. My background is in pure mathematics but I find myself as a physicist/engineer in training. Thanks...
 

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