This will pull the red dot down and raise the weight. If the spool rolls to the right, as above, the point where the string leaves the spool (near point B), will have a somewhat downward motion. Googling, I found a nice description of this by Sunil Kumar Singh at Connexions. The spool’s motion can be described, at least instantaneously, as rotation around that contact point. When the spool rolls (we assume without slipping), the point at the very bottom, where it touches the table, is stationary. Which way can the spool roll so the red dot moves upward? The physics idea is simply that the weight must fall, so the red dot must come closer to the pulley. I put a red dot on the string to help visualize its motion. To see why, let’s imagine that the thread isn’t being pulled by your hand, but by a weight connected to a pulley. In this case, even if the first situation was unclear, you probably know that the spool will roll off to the left. Let’s first examine a different case where the string is pulled up rather than sideways. This method is direct, but it’s useful to find another viewpoint if you can. Torques are actually a pretty easy way to solve this problem, especially if you calculate the torque around the point of contact between the spool and the table (since in that case friction has no moment arm and exerts no torque). The forces you must account for are the force of tension from the string and the force of friction from the table. The usual method is to work it out with torques. Take a minute to see if you can tell how it works. The dashed circle is the inside of the spool and the green line is the thread. You have a spool of thread, already partially unwound. I’ve seen it from time to time since, and here I hope to find an intuitive solution. This problem was on the pre-entrance exam I took before arriving at Caltech for my freshman year.
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