🚀 go-pugleaf

dan@danberg.llnl.gov (Dan Bergmann) writes:
>[The following question is supposedly from an SAT, typically with
> questionable answers because of smart students and not-so-smart 
> question-writers]
>
>Two circles are next to each other and touching at one point (one is NOT
>inside the other). The larger circle has twice the radius of the smaller
>circle. The smaller circle rolls around the large one until it comes back
>to its original starting position. How many revolutions does it make about
>its center?

Given that this question was on the SAT, I'm not surprised.  It seems fairly
obvious to me that the larger circle has a circumference twice that of the
smaller circle.  However, the question asks for the number of "revolutions
about its center".  This raises several options:

1) Revolutions of the larger circle about the larger circle's center --
(since the larger circle is the nearest antecedent of the pronouns "it"
and "its") 0.

2) Revolutions of the smaller circle... -- 0.  "Revolution" implies motion
about a point outside a body.  The center of the smaller circle moves with
the circle, and the circle doesn't even move around the initial location of
the center point.

3) *Rotations* of the larger circle... -- 0. Again, using the nearest
antecedent, and the fact that "rotation" implies motion about a point
interior of the body in question.  Oh, and this also assumes that the frame
of reference for defining a rotation is based on the orientation of the
larger circle (i.e. the large circle doesn't move).

4) Rotations of the smaller circle... -- 3.

Consider the circles joined as: Oo, touching at the larger circle's "east"
point.  Move the smaller circle counter-clockwise.  When the smaller
circle is at "north", it is touching the larger circle with the
point originally at the smaller circle's "east".  Thus, in 1/4
revolution about the larger circle, the smaller circle has made 3/4
rotation (the "east" point has moved counter-clockwise to "south").
Completing the trip, the smaller circle does 4*3/4=3 rotations.

If the question as phrased above is accurately quoted from the SAT, I have
even less faith in the SATs than I did before.  If not, well, pick an
answer.

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