Second Law

You have a spool of rope laying on it's side. The rope is passing under the central axle and to the right toward you. You pull slowly on the rope directly to the right. What will happen? Will the spool roll away from you to the left, or toward you to the right?

Despite the common intuition that such pulling will cause the spool to spin counterclockwise and roll to the left, in fact it will roll to the right (and wind up the rope you are pulling). Try it.

One way to think of why this must be true is through Newton's Second Law of Motion. Newton's second law is one of the most simply stated yet powerfully predictive ideas in physics. It is:

F = M * A

Where F is the force exerted on an object. This is a vector, so it is a direction and a magnitude.
M is the mass of the object.
And A is how the object accelerates, also a vector.

This means that if you pull on the spool to the right (F), and nothing else is pushing or pulling on it*, the acceleration vector (A) must be in the same direction and just scaled by the mass, M.

*Gravity is pulling it down, but the ground is pushing it up just the same, and our pulling is not at all in the same direction, so it shouldn't affect anything. Also friction is pushing left, but by its nature friction can't be greater than our force, F. Since we're just talking about the direction and not magnitude of the motion, it's fine to ignore it.