Math Is Fun Forum

Stanley

Member

Registered: 2006-10-27

Posts: 9

Need to know how?

I have two similar coins, one is kept static and other is revolving the static one without any slip. Can you explain theoretically how many revolutions will be made in the dynamic coin?

Thanks!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Need to know how?

The dynamic coin is “rolling” along the circumference of the static coin, if that’s what you mean? In that case, the dynamic coin will make two revolutions for each complete roll around the static coin.

Try it with real coins and test it for yourself.

Last edited by JaneFairfax (2007-03-10 04:26:14)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Need to know how?

Since you want an explanation as well, I'll try.
If the static coin was just a straight line, then the rolling coin would turn exactly once.
However there is an additional turn thrown in due to the static coin being a circle.

Take note that the direction of rotation of the coin itself (like the Earth spinning), is
also the direction that the coin revolves around the static coin (like the Sun).
I read somewhere that the Earth actually rotates 365.25 plus one turns or minus one turns.
No I think plus one turn.  So it turns 366.25 times from the point of view of being far away
from the solar system looking down upon it.  Because each time there is a new day at
noontime, the Earth has turned more than a single turn, due to the fact that the Earth
has moved seasonally a little bit (about one-ninetieth of a season each day).
Not exactly 90, more like 365.25/4, I think.  Not 366.25/4, because that is extra!!
Think and read about it at:  http://vidyaonline.net/arvindgupta/martingardner.pdf
In this reading link, the Penny Paradox is just a few pages down.

---

igloo myrtilles fourmis