Carl Mungan’s article1 on pulling a spool predicts the directions of the friction force acting on the spool at different pull angles. For quantitative measurements, I used a fishing line spool to measure its linear and angular speeds. Mungan’s results stood firm, but some of the results were very surprising. Each spool in Fig. 1 rotates clockwise and moves to the right since the string in each case exerts a clockwise torque about the contact point P at the bottom of the spool. The center of mass of each spool travels to the right at speed v, each spool rotates at angular velocity ω, and the spool rotates without slipping since v = Rω, where R is the outer radius of the spool.
The first surprise was that the free length of the string sometimes increases and sometimes decreases. In Fig. 1(a), the free length...