Confused question: rotations in rolling coin about another

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mumu416

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Nov 18, 2008
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PLEASE DON"T LAUGHE AT ME i know to you, it's easy...

Well, i don't understand this question in the test, i 'm really confused -
QUESTION
How many times can a coin rotate in rolling completely about another coin of twice the diameter.

A) 2(Pi)
B)2
C)3
D)Pi squared
E)Pi(r)
 
Re: Confused question for me...

Hint: make the diameters 1 and 2.
 


Understanding the term "circumference" and how to calculate its value will also help.

 
These are important questions in celestial mechanics - also for watchmakers (the analog kind that is...).

These types of curves are called epicycloids [or *oids - the * being latin prefixes like card, Ranuncul, etc. - may these are greek]. Your particular curve will be called nephroid. The locus of a point on the rotating coin - will look like a kidney.

Do a little google search - it will be interesting.
 
Yes. I hope you got that by understanding the problem, rather than guessing. When you know the diameter of a coin, the circumference is given by

\(\displaystyle c = \pi d\)

Using Denis's suggestion of setting the diameters to 1 and 2, that gives circumferences of \(\displaystyle \pi\) and \(\displaystyle 2 \pi\).

So, when the smaller coin completes one roll about the larger one, the smaller coin will have gone the distance of its circumference, which is only half the circumference of the larger coin.
 
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