Unification of Newton's laws of motion

2003 ◽  
Vol 81 (5) ◽  
pp. 713-735
Author(s):  
A F Antippa
Keyword(s):  
Second Law ◽  
Mass Scaling ◽  
Self Energy ◽  
The Third ◽  
Inertial Frames ◽  
Third Law ◽  
Newton’S Laws ◽  
Laws Of Motion

Newton's three laws of motion are unified into one law (a slightly modified second law), valid in generalized inertial frames (defined by a slightly modified first law), invariant under mass scaling (guaranteed by the third law), and having important implications for the concept of force and the problem of self-energy. PACS Nos.: 45.20.Dd, 45.50.Jf, 45.05.+x

On the Three Laws of Gearing

2002 ◽  
Vol 124 (4) ◽  
pp. 733-744 ◽  
Author(s):  
David B. Dooner
Keyword(s):  
Direct Contact ◽  
Angular Displacement ◽  
Geometric Theory ◽  
Gear Ratio ◽  
Second Law ◽  
The Third ◽  
Kinematic Geometry ◽  
Third Law ◽  
Conjugate Surfaces ◽  
Contact Mechanism

Three laws of gearing are presented in terms of a three link 1-dof spatial direct contact mechanism. The first law of gearing defines the instantaneous relationship between an infinitesimal displacement of an output body to an infinitesimal angular displacement of an input body for a specified tooth contact normal. A system of cylindroidal coordinates are introduced to facilitate a universal methodology to parameterize the kinematic geometry of generalized motion transmission between skew axes. The second law of gearing establishes a relation between the instantaneous gear ratio and the apparent radii of the hyperboloidal pitch surface in contact as parameterized using a system of cylindroidal coordinates. The third law of gearing establishes an instantaneous relationship for the relative curvature of two conjugate surfaces in direct contact and shows that this relation is independent of the tooth profile geometry. These three laws of gearing along with the system of cylindroidal coordinates establish, in part, a generalized geometric theory comparable to the existing theory for planar kinematics.

The Lex Agraria of 111 B.C. and Procedure in Legislative Assemblies

Antichthon ◽  
1978 ◽  
Vol 12 ◽  
pp. 45-50
Author(s):  
R. Develin
Keyword(s):  
Second Law ◽  
Land Distribution ◽  
The Third ◽  
The Poor ◽  
The Subject ◽  
Third Law ◽  
The Law ◽  
Land Holdings ◽  
Point Of Reference

Agrarian legislation in the immediate aftermath of the Gracchi is the subject of continuing debate. Appian (BC i 27) records three laws, the last two of which are specified as being tribunician: the first removed the inalienability of land holdings; the second was perhaps the measure of Sp. Thorius, mentioned also by Cicero, which stopped land distribution, confirmed possession rights on the land and imposed a rent, the proceeds of which were to help the poor; the third abolished this rent. Appian provides chronological clues of a sort: the first measure came ‘not long after’ the death of C. Gracchus, the third ‘not long after’ Thorius’ law, and the whole business was perhaps finished within fifteen years άπò τῆς Γράκχου νομοϑεσίας. I say ‘perhaps’ because it remains arguable whether the point of reference for these fifteen years is Tiberius or Gaius Gracchus. I intend to argue elsewhere that Tiberius is meant, but as such an argument cannot be regarded as conclusive, there is still a point in this respect in examining the lex agraria which is the inscription CIL i2 585. The law is naturally important in its own right. It is dated internally to 111 B.C. and attempts have been made to equate it with either the second or third of Appian’s laws. If it was the second, this allows a retention of the fifteen years and the placing of the third law in 109 or 108. But if Appian has accurately reported the second law, it imposed a rent, while the first part of the inscriptional law talks of removing rent.

A THEORY OF INNOVATION AND CASE STUDY

2010 ◽  
Vol 14 (05) ◽  
pp. 893-913 ◽  
Author(s):  
NAM P. SUH
Keyword(s):  
Energy Barrier ◽  
Necessary Conditions ◽  
Critical Size ◽  
Government Policies ◽  
Second Law ◽  
Activation Energy Barrier ◽  
Initial Size ◽  
The Third ◽  
Third Law

Three laws of innovation are advanced as the necessary conditions for creating innovations hubs and innovations. The first law states that for innovation to occur, all the required steps of an innovation continuum must be present. The second law states that an innovation hub can be nucleated if the initial size of the nucleate is larger than the critical size and if the activation energy barrier for nucleation can be overcome. Once the innovation hub is nucleated, heterogeneous nucleation of innovation can occur around the innovation hub. The third law states that for innovation to occur, the nucleation rate of innovation must be faster than the rate at which innovative talent and ideas can diffuse away from the region. This theoretical framework has been proposed as a means of formulating government policies for economic growth and innovation. A case study is presented.

scholarly journals Manuais e História da Ciência: a segunda lei de Newton

2019 ◽  
Vol 20 ◽  
pp. 536-549
Author(s):  
Ricardo Lopes Coelho
Keyword(s):  
High School ◽  
Problem Solving ◽  
18Th Century ◽  
Historical Research ◽  
Second Law ◽  
Newton’S Laws ◽  
Conceptual Problems ◽  
Laws Of Motion ◽  
Newton's Second Law

Resumo Aprendemos no liceu e na universidade que a segunda lei de Newton é F=ma. Porém, Newton nunca escreveu a equação. Além disso, não há acordo entre os historiadores da ciência em relação à equação que expressa a segunda lei de Newton. Físicos do séc. XVIII, que citaram e explicaram as leis de Newton, não usaram F=ma. Portanto, se a tese dos manuais contemporâneos fosse correta, teríamos de admitir que todos aqueles físicos interpretaram mal a segunda lei de Newton. Por outro lado, Euler defendeu ter descoberto um novo princípio de mecânica, que é F = ma. Comparando a segunda lei de Newton e o princípio de Euler compreendemos que elas diferem significativamente. Este resultado da pesquisa histórica tem implicações nos problemas conceptuais da mecânica e na resolução de problemas, como iremos ver.Palavras-chave: A segunda lei de Newton; o princípio de Euler; manuais. Abstract We learned at high school and university that Newton’s second law is F=ma. However, Newton never wrote this equation. Furthermore, there is no agreement among historians of science as to the equation that expresses Newton’s second law. 18th century physicists, who quoted and explained Newton’s laws of motion, did not use F=ma. Therefore, if contemporary textbook writers’ claim were correct, we would have to admit that all those physicists misunderstood Newton’s second law. They did not grasp that his law was F=ma. Furthermore, Euler claimed to have discovered a principle of mechanics, which is F=ma. This paper of Euler provides us with the means of clarifying the issue. We can compare Newton’s second law and Euler’s principle with each other and verify whether there are significant differences between both laws. The result is that Newton’s second law is not Euler's principle. This result of historical research has implications for the conceptual problems of mechanics and problem solving, as we shall see. Keywords: Newton’s second law; Euler’s principle; textbooks.

2. Matter from the outside

2014 ◽  
pp. 22-37
Author(s):  
Peter Atkins
Keyword(s):  
Physical Chemistry ◽  
Free Energy ◽  
Gibbs Energy ◽  
Absolute Zero ◽  
Second Law ◽  
Conservation Of Energy ◽  
The Third ◽  
Laws Of Thermodynamics ◽  
Third Law

‘Matter from the outside’ focuses on the applications of thermodynamics in physical chemistry. Thermodynamics is the science of energy and the transformations that it can undergo. It plays a central role in understanding chemical reactions. There are four laws of thermodynamics: the Zeroth Law establishes the concept of temperature; the First Law concerns the conservation of energy; the Second Law deals with entropy (a measure of the quality of energy); and the Third Law concerns the absolute zero of temperature. The property enthalpy is explained along with Gibbs energy and free energy. Physical chemists can deploy the laws of thermodynamics, laws relating to matter from the outside, to establish relations between properties and to make important connections.

The Third Law in Newton's Mechanics

1968 ◽  
Vol 4 (1) ◽  
pp. 39-51 ◽  
Author(s):  
Roderick W. Home
Keyword(s):  
Operational Definition ◽  
Historical Aspects ◽  
The Third ◽  
The World ◽  
The Status ◽  
The Subject ◽  
Third Law ◽  
Newton’S Laws ◽  
Philosophical Viewpoint ◽  
Definition Of

Most modern analysts of Newton's laws of motion, whether they have approached the subject from a historical or from a philosophical viewpoint, have tended to concentrate on the status of the first two laws; the third law has largely been overlooked, or else it has been dismissed as somehow less interesting. My purpose in this paper is to reverse this approach—I intend to investigate some of the historical aspects of the third law, particularly the empirical background to Newton's statement of it, and in so doing, I intend to skirt most of the questions which have been raised concerning the status of the other two laws. In concentrating on the historical aspects of the third law, I shall also by-pass Mach's controversial re-interpretation of its role in mechanics, for while Mach saw the law as the basis for an operational definition of “mass”, it is quite clear that Newton did not so regard it. On the contrary, Newton seems to have regarded all three of his laws as straightforward statements of fact about the world, so that a knowledge of the factual background to the laws is a fundamental pre-requisite to an understanding of Newton's thought.

The Second Law of Thermodynamics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Second Law Of Thermodynamics ◽  
Worked Examples ◽  
Phase Changes ◽  
Second Law ◽  
The Third ◽  
Mathematical Properties ◽  
Third Law Of Thermodynamics ◽  
Third Law ◽  
Definition Of ◽  
Clausius Inequality

The Second Law. The definition of entropy, and its mathematical properties. The Clausius inequality, and the criterion of spontaneity of change in an isolated system. Worked examples of heat flow down a temperature gradient, and the adiabatic expansion of a gas into a vacuum. Combining the First and Second Laws, with worked examples, such as phase changes. Introduction to the Third Law of Thermodynamics. Introduction to T,S diagrams.

Changing the Order of Newton's Laws—Why & How the Third Law Should be First

2012 ◽  
Vol 50 (7) ◽  
pp. 406-409 ◽  
Author(s):  
Sue Stocklmayer ◽  
John P. Rayner ◽  
Michael M. Gore
Keyword(s):  
The Third ◽  
Third Law ◽  
Newton’S Laws
Sign in / Sign up

Export Citation Format

Share Document