Consider a pair of identical (typical) screws and held in opposite hands: the right pointed to your left, the left pointed to your right.

Then place them adjacent to each other (the one in your right hand "on top"), and "interleave" their helical threads together.

If I move the bolts around each other as one would twiddle ones thumbs (the top one comes toward you and the bottom one away from you), holding each screw firmly by the head so that it does not rotate, do the heads:

a) move inward
b) move outward
c) remain the same distance from each other?

You should determine the answer without resorting to the actual test

I remember this problem from somewhere in the past ("twiddled bolts"), but fortunately I can't remember the answer at all.

If I picture one screw, pointing to the right, and then imagine a stylus rather than a second screw... the stylus is perpendicular to the shaft of the screw and the stylus point engages between 2 threads into a valley.  Now picture moving the stylus in a circle, the axis of the motion is in the center of the core of the screw.  Then it seems to me that the screw would have to move either left or right depending on the direction of circular movement.

BUT, if you consider twiddling two screws, R and L, then picture from the frame of reference of first the R screw, as if it were stationary, sighting from its head towards its point, then the L screw appears to be moving counterclockwise around the R screw.   But switch the frame of reference to the head of the L screw, and the R screw appears to be moving clockwise around the R screw.

So my conclusion is that the screws must stay the same distance apart since they can't be moving both towards each other and away from each other at the same time.  (Because one screw is moving towards the other at the same rate the other screw is moving away)

(I did look down at my thumbs, as I twiddled them, so this may have been partial cheating)

Posted by Larry on 2004-12-25 18:56:40