Session:

A Potpourri of Astronomy and Physics Topics

Paper Type:

Contributed

Title:

Balls Rolling in Cones: Newish Examples of LearningbyContrast

Meeting:

2014 Winter Meeting: Orlando, Florida 
Location:

N/A 
Date:


Time:

4:50PM

Author:

Gary Dane White, AAPT and GWU
3012093314, gwhite@aapt.org

CoAuthor(s):

None

Abstract:

The motion of a ball rollingwithoutslipping 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 planetsor notby carefully selecting the conical angle and the ball's moment of inertia. Learningbycontrast, 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)

Footnotes:

*see "The shape of 'the Spandex' and orbits upon its surface", Gary D. White and Michael Walker, Am. J. Phys. 70, 48 (2002)

Presentation:

Cone talk AAPT orlando for website_White.pdf

