![]() ![]() A crate whose mass m is 360 kg rests on the bed of a truck that is moving at a speed v0 of 120 km/h, as in Fig. ![]() An improved physical description of the acceleration of a particle is obtained if it is viewed in terms of the Frenet–Serret frame. The author does not intend to slight these excellent pedagogical efforts, but feels an improved treatment is possible using a junior physics major’s knowledge of basic calculus. One possible reason is that the mathematical treatment in classical mechanics texts relies on relatively simple arguments involving Cartesian or polar coordinates that are not naturally adapted to the curve describing the general motion of a particle. In most textbooks, the concept of centripetal acceleration appears as a separate concept that is not tied to the general acceleration concept, and is often presented as an artifact of circular motion rather than a consequence of the generalized motion of a particle. The concept of acceleration is developed as the rate of change of velocity with special cases (e.g., centripetal acceleration) developed to describe particular types of motion (e.g., circular motion). Introduction Classical mechanics textbooks universally address particle motion and associated quantities such as acceleration. PACS numbers: 01.30.Rr, 01.40.-d, 02.40.Hw UDC 531.122 Keywords: particle’s motion, Frenet–Serret frame, centripetal acceleration 1. Within this frame, centripetal acceleration emerges as a natural consequence of a particle’s motion. ![]() E-mail address: Received 6 October 2003 Accepted 15 December 2003 Online 19 April 2004 A clear physical description of a particle’s motion in terms of the components of its acceleration is obtained if the trajectory is described in terms of the Frenet–Serret frame. ISSN1330–0008 CODENFIZAE4 EMERGENCE OF CENTRIPETAL ACCELERATION WITHIN THE FRENET–SERRET FRAME JOSEPH JOHN BEVELACQUA Bevelacqua Resources, Suite 100, 343 Adair Drive, Richland, WA 99352 U.S.A. ![]()
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