Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T15:36:45.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Conics and a generalised conical pendulum

Published online by Cambridge University Press:  14 February 2019

Daniel Daners  and
Theresa Wigmore
Daniel Daners
Affiliation:
School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia e-mail: [email protected]
Theresa Wigmore
Affiliation:
Ravenswood School for Girls, PO Box 516, Gordon, NSW 2072, Australia e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

There is a long tradition of using geometry to solve problems from mechanics. Unfortunately this tradition is not practised much in schools and university any more.

With this exposition we would like to demonstrate how elementary properties of ellipses can be used to solve a problem related to the conical pendulum. The problem of the conical pendulum is to consider a mass attached to one end of a light inextensible string of length with the other end attached at the top of a vertical rod. The mass is moving about the rod in uniform circular motion in a horizontal plane. Given the angular velocity of the mass, the question is to determine the angle the string makes with the rod.

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 556 , March 2019 , pp. 28 - 40
Copyright
Copyright © Mathematical Association 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Akopyan, A. V. and Zaslavsky, A. A., Geometry of conics, Mathematical World, 26, Amer. Math. Soc. (2007).10.1090/mawrld/026Google Scholar
2. Glaeser, G., Stachel, H. and Odehnal, B., The universe of conics: From the ancient Greeks to 21st century developments, Springer Spektrum, Berlin (2016).10.1007/978-3-662-45450-3Google Scholar
3. Arnold, D. and Arnold, G., Cambridge Mathematics 4 Unit, Cambridge University Press (2000).Google Scholar
4. Berendonk, S., Proving the reflective property of an ellipse, Mathematics Magazine 87 (2014) pp. 276–279.10.4169/math.mag.87.4.276Google Scholar
5. Brozinsky, M. K., Reflection property of the ellipse and the hyperbola, The College Mathematics Journal 15 (1984) pp. 140–142.10.2307/2686519Google Scholar