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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: daniel.daners@sydney.edu.au
Theresa Wigmore
Affiliation:
Ravenswood School for Girls, PO Box 516, Gordon, NSW 2072, Australia e-mail: twigmore@ravenswood.nsw.edu.au
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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 

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References

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