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Two Discs, One Rotating

Date: 7/5/96 at 22:34:4
From: Frank Leung
Subject: Two Discs, One Rotating

Two circular discs have radii 8 cm and 28 cm. The larger disc is fixed 
while the smaller disc rolls around the outside of the larger. In 
their original positions, point A on the smaller disc coincides with 
point B on the larger disc. What is the least number of rotations that 
the small disc makes about its centre before A and B coincide again?

Date: 7/6/96 at 7:42:18
From: Doctor Anthony
Subject: Re: Two Discs, One Rotating

If we consider where the lengths of the circumferences will match for 
complete revolutions, we see that 7 revolutions on the smaller disc 
will correspond to 2 revolutions on the larger disc.  i.e. 7*8 = 2*28

The smaller disc therefore completes 7 rotations if it were rolling 
along a straight line, but 2 more rotations because it is going round 
the larger disc.  

Total number of complete rotations = 7 + 2 = 9 about its centre.

-Doctor Anthony,  The Math Forum
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Associated Topics:
High School Conic Sections/Circles
High School Euclidean/Plane Geometry
High School Geometry

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