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Exploring Circle Rotation
Question: Two
circles(r1, r2) of radius 10, and 25 are touching each
other and spins without slippage. when r1 is spinning at 50 rpm, at
what rpm is r2 spinning?
Answer: The key is to
realize that as circle 1 turns so does circle 2, each moves along the same
distance along their circumferences (since there is no slippage and they can be
tangent at a single common point each instant).
So,
one revolution of circle one corresponds to a distance along its circumference
equal to 2πr1 The distance along the circumference along circle 2 is
the same and represents 2πr1 / 2πr2 = r1 /
r2 of one revolution of circle 2. If every minute circle 1 revolves
50 complete revolutions then circle 2 must revolve (r1 / r2
)* 50 = (10 / 25 )* 50 = 20 revolutions.
This is another FREE GEOMETRY PRINTABLE presented to you from the
Geometry section of
K12math.com
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