Session:
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A Potpourri of Astronomy and Physics Topics
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Paper Type:
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Contributed
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Title:
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Balls Rolling in Cones: New-ish Examples of Learning-by-Contrast
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Meeting:
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2014 Winter Meeting: Orlando, Florida |
Location:
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N/A |
Date:
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Time:
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4:50PM
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Author:
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Gary Dane White, AAPT and GWU
301-209-3314, gwhite@aapt.org
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Co-Author(s):
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None
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Abstract:
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The motion of a ball rolling-without-slipping on a conical surface reveals many analogies with classical celestial phenomena, and many contrasts as well. The initial conditions of the ball's "spin" can be adjusted so that one can observe quite different orbital periods even at a fixed orbital radius! Even so, the analogy with Kepler's Third Law--"(period squared)/(radius cubed) = constant"--is robust; for a ball rolling in a cone the dictum is "(period squared)/(radius) = constant," providing a nice contrast with real gravity, and with balls rolling in spandex wells for which the mandate is "(period cubed)/(radius squared) = constant," curiously.* Furthermore, one can choose to mimic the closed elliptical orbits of the planets--or not--by carefully selecting the conical angle and the ball's moment of inertia. Learning-by-contrast, at least for this author, is effective, and its benefits far outweigh any disappointment that celestial phenomena are not reproduced precisely. *see "The shape of 'the Spandex' and orbits upon its surface", Gary D. White and Michael Walker, Am. J. Phys. 70, 48 (2002)
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Footnotes:
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*see "The shape of 'the Spandex' and orbits upon its surface", Gary D. White and Michael Walker, Am. J. Phys. 70, 48 (2002)
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Presentation:
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Cone talk AAPT orlando for website_White.pdf
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