The Coin Problem

[Cyrealist]

Next problem: explain how planetary gears work.

 

[jmb]

Thread mash. How many of these coins will
It take to buy a used luxury car.

 

[Drew0311]

I just eye balled it and said 4. Then tried to math it and failed. So when I saw four wasn’t an answer I knew I was wrong. Then got proven right. I drank way to much last night for this ****.

 

[KidSilverhair]

Ok, but can the coin take off?

Well, if you’re rotating these coins on a treadmill all bets are off.

 

[cstrunk]

What if you spray the coins with spam and place them on a treadmill?

 

[intrepid27]

Ok, but can the coin take off?

No. But when it gets to the bottom half, gravity will take over and it will fall off. Thus there is no correct answer.

 

[engineer_doug]

Don't forget inflation, so maybe 5 revolutions is needed instead of 4...

 

[Steve]

What is easily missed is that the small coin path is not around the circumference of the large coin. It is actually around the sum of the radius of the large coin plus the radius of the small coin.

 

[Acylum]

Next problem: explain how planetary gears work.

I’ve watched YT videos and still can’t grasp it.

 

[dafarmer]

Problem shows radius of 3 and 1 inch. Circumference of 3 divided by 1 = 3. Put it on a flat surface. The radius of a 3 inch circle is .478 and radius of a 1 inch circle is .159.

 

[JustBecause]

Problem shows radius of 3 and 1 inch. Circumference of 3 divided by 1 = 3. Put it on a flat surface. The radius of a 3 inch circle is .478 and radius of a 1 inch circle is .159.

The answer would be 3 if it was on a flat surface. It’s 4 because it’s not a flat surface.

 

[amishclone]

No. That’s the gotcha of the problem and is not correct.

I don't follow

 

[Jeremy]

Entered thread, saw you have to use brain, leaving immediately.

 

[FDWxMan]

Think about it from the perspective of the center of the small coin.

Yes, its circumference is 1. If you roll it on a flat surface for three inches, the center travels 3 inches, in a straight line

But think about how far the center is traveling when it goes around the big circle. The center is now traveling in a circle, and that circle's circumference has changed.

Instead of moving in just a straight line, equal to the circumference of itself 2*pi*r = 1, the center is now moving in a circle with a circumference of 2*pi*(R+1) = whatever (more than 1). That is where the extra movement is coming from.

 

[Die4Cy]

This gave me a headache.
View attachment 107389

 

[Acylum]

Think about it from the perspective of the center of the small coin.

Yes, its circumference is 1. If you roll it on a flat surface for three inches, the center travels 3 inches, in a straight line

But think about how far the center is traveling when it goes around the big circle. The center is now traveling in a circle, and that circle's circumference has changed.

Instead of moving in just a straight line, equal to the circumference of itself 2*pi*r = 1, the center is now moving in a circle with a circumference of 2*pi*(R+1) = whatever (more than 1). That is where the extra movement is coming from.

This is the explanation I found which then took me down the sidereal orbital period rabbit hole.

 

[dafarmer]

Circumference is 3, doesn’t make any difference about the center. Put a 3 inch line on a surface and a 1 inch line next to it.

 

[tm3308]

**** this. Just give me the damn coins so I can do my laundry.

 

[urb1]

Math is hard. Let's go shopping.

 

[Rogue52]

Please tell me there was someone who missed out on a perfect SAT score because he left the answer blank and got everything else correct.