AAPT Logo
TPT Logo
 
   
 

You are not logged in You are not logged into this journal. Log In

The Physics Teacher -- December 2011 -- Volume 49, Issue 9, pp. 576

Figuring the Acceleration of the Simple Pendulum

Martin Lieberherr

Mathematisch Naturwissenschaftliches Gymnasium Rämibühl, Physikalisches Institut, Zürich, Switzerland

Full Text: Read Online (HTML) | Download PDF | Buy PDF (US$30) | View Cart
The centripetal acceleration has been known since Huygens' (1659) and Newton's (1684) time.1,2 The physics to calculate the acceleration of a simple pendulum has been around for more than 300 years, and a fairly complete treatise has been given by C. Schwarz in this journal.3 But sentences like “the acceleration is always directed towards the equilibrium position” beside the picture of a swing on a circular arc can still be found in textbooks, as e.g. in Ref. 4. Vectors have been invented by Grassmann (1844)5 and are conveniently used to describe the acceleration in curved orbits, but acceleration is more often treated as a scalar with or without sign, as the words acceleration/deceleration suggest. The component tangential to the orbit is enough to deduce the period of the simple pendulum, but it is not enough to discuss the forces on the pendulum, as has been pointed out by Santos-Benito and A. Gras-Marti.6 A suitable way to address this problem is a nice figure with a catch for classroom discussions or homework. When I plotted the acceleration vectors of the simple pendulum in their proper positions, pictures as in Fig. 1 appeared on the screen. The endpoints of the acceleration vectors, if properly scaled, seemed to lie on a curve with a familiar shape: a cardioid. Is this true or just an illusion?

© 2011 American Association of Physics Teachers

Acknowledgments

I would like to thank an anonymous reviewer for his comments and valuable guidance.

KEYWORDS and PACS

Keywords

acceleration, pendulums, physics education, vectors

PACS

  • 01.50.-i

    Educational aids

  • 07.10.-h

    Mechanical instruments and equipment

  • 45.05.+x

    General theory of classical mechanics of discrete systems

PUBLICATION DATA

ISSN

0031-921X (print)  

Publisher

$abstract.society.value is a Member of CrossRef American Association of Physics Teachers

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.3661108

For access to fully linked references, you need to log in.

Figures (5)

Access to article objects (figures, tables, multimedia) requires a subscription; log in to view available files.
(Access to supplementary files, where available, is free for this journal.)



Close

Your Recent History Recent History Help

Recently Viewed

  1. Figuring the Acceleration of the Simple Pendulum
  2. Laboratory Activity: Specific Heat by Change in Internal Energy of Silly Putty
  3. Non-Mathematical Explanation of Precession
  4. Jogging on a Carousel
  5. Leadership in Freshman Physics

AAPT on:

close