Originally Posted by
jimmuller
You're right that the spindle doesn't touch the cup. But the bearings "going the opposite direction" isn't why the cup can unscrew. In fact, there is little or no friction between spindle, bearings, and cup. ...
I'm not sure about your explanation. In normal operation the cup doesn't rotate in the shell. Your circle-in-circle description doesn't explain where the force comes from that makes a right-threaded fixed cup want to break loose from its grip on the threads of the shell and start turning.
There may not be any rolling friction between spindle and bearings, or between bearings and cup, but there is thrust, from the "grip" between the moving parts. (If there was no grip, the balls would not roll when the spindle rotated in contact with them. The spindle would just slide over them. But because balls on polished steel have such low rolling friction, very small amounts of thrust will make them turn.) And it's that thrust that makes pedaling action want to turn the cup: the spindle turns the balls, and the balls (try to) turn the cup.
Think of the steel wheels of a train locomotive resting on a steel rail: very low rolling friction -- what there is comes from the slight deformation of the rail and the wheel at their point of contact by the weight of the locomotive. But when the engineer applies power, the wheels thrust against the rail and start the train moving. (If there was no grip, the wheels would just spin.) Where heavy trains climb steep grades, such as from Field, B.C., up to the Continental Divide at Stephen, this thrust against the rails causes them to creep downhill perceptibly enough to be a track maintenance issue, despite all those thousands of spikes holding them down to the ties.
You can demonstrate this "bearing precession" effect at home: Take two cups, some dry balls (no grease), and a spindle. Assemble the parts as if they were going into a bike but hold the spindle vertically so that one cup floats freely on the "top" race of the spindle as if it were a hat. Now, holding the lower cup with one hand to keep things steady, contrive to spin the spindle with a variable-speed electric drill. At a very low speed, the top balls will stay "stuck" to spindle and cup so the top cup rotates the same direction as the spindle. As you spin the spindle faster, so that your thrust becomes enough to start moving the balls, the floating cup starts to lag behind the spindle, then stops, then begins to move ever faster in the opposite direction.
Q.E.D.