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ERIC Number: EJ951131
Record Type: Journal
Publication Date: 2011-Dec
Pages: 2
Abstractor: As Provided
Reference Count: 8
ISSN: ISSN-0031-921X
Figuring the Acceleration of the Simple Pendulum
Lieberherr, Martin
Physics Teacher, v49 n9 p576-577 Dec 2011
The centripetal acceleration has been known since Huygens' (1659) and Newton's (1684) time. 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. 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) 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. 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?
American Association of Physics Teachers. One Physics Ellipse, College Park, MD 20740. Tel: 301-209-3300; Fax: 301-209-0845; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A