Two Discs, One RotatingDate: 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/ |
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