Help with the problem of moving two fingers along a yardstick

The following problem is taken from an MIT homework assignment:

Hold a yardstick horizontally on your index fingers and slide your fingers together smoothly. The stick slides first on one finger, then on the other and it keeps alternating. This was demonstrated in lectures. Try it for yourself, it’s great fun! Why does this happen?

This question has already been asked elsewhere, but I have a question specifically about the MIT solution:

Let $$N_1$$ and $$F_1$$ be the normal and frictional forces for one finger, and let $$N_2$$ and $$F_2$$ be the normal and frictional forces for the other finger. The key to understanding this problem is to realize that the fraction of weight supported by each finger can be different. Clearly, the finger closest to the center of the yardstick will bear a larger fraction of the weight and hence will exert a larger normal force on the yardstick.

Imagine starting each finger under a separate end of the yardstick. Initially, each finger shares the weight equally, but as you attempt to move your fingers one of them, say finger 1, starts to slide. (To avoid sliding you would have to start with your fingers exactly the same distance from each end and move with exactly the same speed. Clearly human fingers are not capable of this. And the yardstick itself is too irregular for that precision). Immediately after finger 1 slides, both fingers will share the same weight equally ($$N_1 = N_2$$) but because the kinetic coefficient of friction is less than the static coefficient the friction on finger 2 is greater than the friction on finger 1. As finger 1 continues to slide in, it will bear more of the weight of the yardstick until $$N_1$$ is large enough that $$F_1 = F_2$$. As finger 1 moves in just a bit more, finger 2 will no longer be able to sustain the frictional force from 1, and hence finger 2 will move and finger 1 will stop. The whole procedure will begin again.

I do not understand this last part that I made bold. How does the frictional force on 1 relate in any way to what 2 is experiencing? What do they mean by "it cannot sustain"?

• – dmckee Jul 13 at 14:05
• @dmckee Thank you for your answer. I did come across that post, but I was wondering if I could get a clarification on this explanation – user10796158 Jul 13 at 14:18
• Usually when people comment related post links they are not for the OP's benefit but more for future readers' benefit. If @dmckee thought that answered your question they would have marked it as a possible duplicate instead. – Aaron Stevens Jul 13 at 16:13

• @user10796158 Coefficients of friction and friction forces are different things. Keep in mind for static friction $F\neq\mu_s N$ in general. $\mu_sN$ is just the maximum value it can have. Think of a book sitting on a table. The static friction force acting on the book is $0$, even though $\mu_sN\neq0$ – Aaron Stevens Jul 13 at 17:24