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Circle Revolutions

Date: 07/02/2002 at 12:29:18
From: Fadi Maalouf
Subject: circles


Hello.

I'm a High school student and our teacher has given us a problem none
of us can solve. She gave everyone a CD, and told us to look at the
spin of the smaller inner circle and of the large outer circle. We
have concluded that they both make a revolution in the same amount of
time, but the circumference of the outer circle is greater than the
circumference of the inner circle, so are they moving at different 
speeds? Is that possible? 

Any help you can give me would be great. 

Thank you,
Fadi Maalouf


Date: 07/02/2002 at 21:41:37
From: Doctor Ian
Subject: Re: circles


Hi Fadi,

It's not only possible, it's true.  The angular speeds are the 
same, but the linear speeds are different.  Each time the CD 
rotates, a point at some distance R from the center moves in a 
circle, right?  So the distance he moves is the circumference of 
the circle... and the circumference depends on R.  

Larger distance, larger speed.  

Think of it this way.  Suppose you and a friend are going to run 
a race around a circular track - the first to make it around the 
track one time wins, but you have to stay in the lane you started 
in.  

Would you rather have the inner lane, or the outer one?  Why?  
You're both going to run 360 degrees, right? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Conic Sections/Circles

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