# Which Direction Will It Turn? 1 OR 2 ;)

Discussion in 'Math' started by micro1, Nov 29, 2017.

1. ### micro1 Thread Starter Member

Feb 22, 2015
76
1
Which Direction Will It Turn? 1 OR 2

cmartinez likes this.

Sep 9, 2010
15,525
5,741
1

3. ### whitehaired novice Member

Jul 15, 2017
257
34

Jul 18, 2013
16,832
5,006
I vote 1 also.
Max.

Jul 7, 2017
45
5
6. ### WBahn Moderator

Mar 31, 2012
23,556
7,208
I went through it pretty quickly, but I got 2.

cmartinez likes this.

Jul 18, 2013
16,832
5,006
I actually posted 2 the first time and changed it, I think now I was wrong after another check.2
Max.

Jun 4, 2014
7,045
1,690

9. ### cmartinez AAC Fanatic!

Jan 17, 2007
5,653
6,862
It's #1 ... if the number of gears is odd, then the resulting direction is the same as the first gear, if it is even it's the opposite.
5 groups of gears: odd, odd, odd, even, even. If they were all connected together, the resulting motion would be counterclockwise, but the groups are connected by belts. In the case of groups 2, 3 and 4, they're connected by crossed-belts, which act in the same direction as if they were gears. So group 2, 3 and 4 can be considered as a single unit consisting of 12 gears (even).

That leaves us with three groups: odd, even and even. The three are connected by straight (uncrossed) belts, so the resulting direction of motion at the end of each group will be the starting direction of motion of the next group:

• Group #1: (odd) start ccw, end: ccw
• Group #234: (even) start: ccw, end: cw
• Group #5: (even) start: cw, end ccw

The resulting motion is counterclockwise in the last gear, which will point to "1"

Another simpler way of looking at it is to add all the gears, and then to ignore the number of crossed belts, but to add another gear to the count for each straight belt. There are 17 gears total, and we add two more (virtual) gears because of the number of straight belts, giving us a total of 19, which is an odd number... therefore the resulting motion will be in the same direction as the first gear...

EDIT: Aaaarggghhh! ... it points at #2! ... but the resulting motion is STILL counterclockwise!

Last edited: Nov 29, 2017
10. ### RichardO Late Member

May 4, 2013
2,273
892
Wheeler said, "Yesterday, Feynman convinced me that it went around backwards.
Today, he's convinced me equally well that it goes around the other way. I
don't know what he'll convince me of tomorrow.

(Quote about backwards sprinkler problem presented in "SURELY YOU'RE JOKING,
MR. FEYNMAN!" by Richard P. Feynman).

cmartinez likes this.
11. ### cmartinez AAC Fanatic!

Jan 17, 2007
5,653
6,862

Jul 18, 2013
16,832
5,006
I did the same thing, but it is easiest if you state the rotation as you proceed through, i.e. CCW, CW, CCW,CCW, CW etc etc.
Max.

13. ### cmartinez AAC Fanatic!

Jan 17, 2007
5,653
6,862
For this example, yeah... but what if it were a far larger number of gears?

Jul 18, 2013
16,832
5,006
I am trying to imagine where a far larger number would be used or desirable?
There are some fairly neat modern alternatives.
Max.

15. ### cmartinez AAC Fanatic!

Jan 17, 2007
5,653
6,862
Yeah... but would your alternative be more fun than an apparatus involving a monkey dressed as a bell boy? Uh? ...

16. ### wayneh Expert

Sep 9, 2010
15,525
5,741
Rats, I answered too quickly. I agree it's 2. It's the same direction on every odd number of gears, and there are 17.

The two reversing pulleys (not crossed, which are just like gears) cancel each other out. I think I would have thought about my first answer longer - and maybe gotten it right - if there had been only one reversal. I saw two and didn't think any more about it.

Jul 18, 2013
16,832
5,006
Wanted: Organ Grinders assistant.
They don't use the real thing anymore, sign of the times.
Max.

cmartinez likes this.

Jul 5, 2008
1,708
338
its 2