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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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Euclidean/Plane Geometry
High School Geometry

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