Dare to Step on This Binomial Expansion Problem

Classical Mechanics Level pending

A cable spool of mass M, radius R and moment of inertia I = βMR2 around an axis through its center of mass is wrapped around its outer disk with fishing line and set on a rough rope as shown. The fishing line is then pulled with a force of magnitude F to the right as shown so that it rolls down the rope on the spool at radius r to the right without slipping.

What is the direction of static friction as it rolls?

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