Physics
Physics of Motion
The physics of motion deals with the study of the movement of objects and the forces that cause them to move. It encompasses concepts such as velocity, acceleration, and momentum, and is governed by Newton's laws of motion. Understanding the physics of motion is essential for explaining and predicting the behavior of objects in the physical world.
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11 Key excerpts on "Physics of Motion"
- Andrei D. Polyanin, Alexei Chernoutsan(Authors)
- 2010(Publication Date)
- CRC Press(Publisher)
Chapter P1 Physical Foundations of Mechanics Preliminary remarks. Mechanical motion is change in the location of a body with respect to other bodies. This definition implies that mechanical motion is relative. In order to describe motion, one should specify a frame of reference , which includes a body of reference, a coordinate system fixed relative to the body, and a set of clocks synchronized with one another. Mechanics studies motions of model objects, a point particle (or a point mass) and a rigid body. The location of these objects is determined by a finite set of independent parameters; the objects are said to have finitely many degrees of freedom . Kinematics deals with the characterization of motion without finding out its reasons. P1.1. Kinematics of a Point P1.1.1. Basic Definitions. Velocity and Acceleration ◮ Point particle. Law of motion. Path, distance and displacement. A body whose dimensions can be neglected in studying its motion (compared to the distances of its movement) is called a point particle (or just a particle ). The position of a point particle at an instant of time t is determined by the position vector r from the origin of some reference frame to the particle (see Fig. P1.1). As the particle moves, the end of the position vector traces a spatial curve, a path (also called a trajectory ). In a rectangular Cartesian reference frame, the position vector is determined by its projections onto the coordinate axis, its x -, y -, and z -coordinates. The motion of a particle is completely determined by specifying its law of motion , a single vector function r ( t ) or three scalar functions x ( t ), y ( t ), z ( t ). A position vector (or any other vector) can be conveniently written in terms of its projections using unit vectors, i , j , and k , of the respective coordinate axes as follows: r = x i + y j + z k . The distance traveled by the particle in a given time interval is measured along the curvilinear path.
eBook - PDF- James Shipman, Jerry Wilson, Charles Higgins, Bo Lou, James Shipman(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
28 CHAPTER 2 Did You Know? Section Speed and velocity are different physical quantities. 2.2 A race car going around a circular track at a constant speed is accelerating. 2.4 A football quarterback cannot throw a “straight-line” pass. 2.5 Motion Give me matter and motion, and I will con- struct the universe. ● René Descartes (1596–1650) Robert Harding World Imagery/Robert Harding/Alamy Stock Photo H aving been introduced to measurement and units, you are ready to begin your study of physics. Physics, the most fundamental physical sci- ence, is concerned with the basic principles and concepts that describe the workings of the universe. It deals with matter, motion, force, and energy. There are various areas of physics: ● ● Classical mechanics is the study of the motion of objects moving at relatively low speeds. ● ● Waves and sound is the study of wave motion and its application to sound. ● ● Thermodynamics is the study of temperature, heat, and thermal processes. ● ● Electromagnetism is the study of electricity and magnetism. ● ● Optics is the study of the properties of light, mirrors, and lenses. ● ● Quantum mechanics is the study of the behavior of particles on the microscopic and submicroscopic levels. ● ● Atomic and nuclear physics is the study of the properties of atoms and nuclei. ● ● Relativity is the study of objects traveling at speeds approaching the speed of light. We will delve into all of these areas, except relativity, and begin with classical mechanics and the study of motion.
- Arthur Haas, T. Verschoyle(Authors)
- 2020(Publication Date)
- De Gruyter(Publisher)
INTRODUCTION TO THEORETICAL PHYSICS PART I MECHANICS TYogether with the General Theory of Vector Fields, ot Vibrations, and of Potential CHAPTER I THE MOTION OF A FREE MATERIAL PARTICLE § 1. The Principle of Inertia, and the Conception of Force. THE simplest form of motion is rectilinear motion in which equal distances are traversed in equal times ; such motion is termed uniform. The velocity of motion is defined as the ratio of any given length of the path to the time required in traversing it, and, in the case of uniform motion, its value remains constant and independent of the length of path considered. If, now, a body describes an entirely arbitrary path, which will in general be curved, and if its motion is likewise arbitrary, then for a short length of path, the motion can also be regarded as being approximately uniform. The shorter the length we consider, the closer the approximation of the imaginary uniform and rectilinear motion to the actual non-uniform and curved motion between two neigh-bouring points along the path. Hence if ds is the element of length along the path which is described in the element of time dt, we may define the differential coefficient dsjdt as the instantaneous value of the velocity. We may also ascribe an instantaneous direction to the velocity, namely, the direction of the element of length, or in other words, that of the tangent to the path. The first fundamental principle of mechanics is the principle of inertia, originally propounded by Descartes (1644) and later formulated by Newton (1687) as the First Law of Motion -1 According to this law, every body maintains its 1 The principle of inertia is really due to Galileo. He originated the concep-tion of ideal motion free from all obstacles, and created for this ideal motion a supreme axiom in the principle of the complete reversibility of the ideal mechanical process.
eBook - PDF- Bogdan Skalmierski(Author)
- 2013(Publication Date)
- Elsevier(Publisher)
CHAPTER 2 The Dynamics of a Particle 2.1 Fundamental definitions and theorems In this chapter we shall discuss the dynamic aspects of a particle in motion. We begin with the basic laws of dynamics. Axioi 1 (Newton's second law). If a force P acts on a particle, the acceleration thus produced is proportional to that force, which can be written as follows: P= m a, (1) where m is the mass of the particle. We shall treat mass as a primary concept. The force P should be regarded as the resultant of the forces acting on the particle, that is, n P = R j . (la) f= 1 The cited law brings into association three basic concepts (force, mass and motion) of mechanics. It is valid in inertial systems (see Chapter 5). Under the SI system, the unit of force is the newton: 1 kgms -2 = 11. For a unit of force we can also take the force with which the earth attracts 1 kg of mass: 1 kgf = 1 kg • g, where g = 9.80665 m s — 2 and is the normal value of acceleration of gravity. The equality sign is valid between inert and heavy mass. Axioi 2 (Newton's third law). If a particle A acts on another particle B with force P AD , then simultaneously B acts on A with force PBA of equal absolute value but with an opposite sense, i.e. R A B + PBa = = 0 . (2) (4) a V P i = 70 THE DYNAMICS OF A PARTICLE Ch. 2 This is known as the law of action and reaction. We shall now introduce the definition of work. By work one should understand a process in which resistance is being overcome along a certain route. This definition is, however, imprecise, and for that reason it is better to define work in concise mathematical notation: Work analytically formulated is a curvilinear integral df B W = P • ds . (3) A If under the integral (3) a total differential occurs, then the forces doing the work are said to have potential V. A decrease in potential is tantamount to an increase in work: — ~ V = d W. Therefore Potential forces, as it will easily be seen, act in the direction of the maximum drop of the potential.
eBook - PDFMeriam's Engineering Mechanics
Dynamics
- L. G. Kraige, J. N. Bolton(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Kinematics is often described as the “geometry of motion.” Some en-gineering applications of kinematics include the design of cams, gears, linkages, and other machine elements to control or produce certain desired motions, and the calculation of flight trajectories for aircraft, rockets, and spacecraft. A thorough working knowledge of kinematics is a prerequisite to kinetics, which is the study of the relationships between motion and the corresponding forces which cause or accompany the motion. Particle Motion We begin our study of kinematics by first discussing in this chapter the motions of points or particles. A particle is a body whose physical dimensions are so small com-pared with the radius of curvature of its path that we may treat the motion of the particle as that of a point. For example, the wingspan of a jet transport flying be-tween Los Angeles and New York is of no consequence compared with the radius of curvature of its flight path, and thus the treatment of the airplane as a particle or point is an acceptable approximation. CHAPTER OUTLINE 2/1 Introduction 2/2 Rectilinear Motion 2/3 Plane Curvilinear Motion 2/4 Rectangular Coordinates ( x -y ) 2/5 Normal and Tangential Coordinates ( n -t ) 2/6 Polar Coordinates ( r -𝜽 ) 2/7 Space Curvilinear Motion 2/8 Relative Motion (Translating Axes) 2/9 Constrained Motion of Connected Particles 2/10 Chapter Review 16 Article 2/2 Rectilinear Motion 17 We can describe the motion of a particle in a number of ways, and the choice of the most convenient or appropriate way depends a great deal on experience and on how the data are given. Let us obtain an overview of the several methods developed in this chapter by referring to Fig. 2 ∕ 1 , which shows a particle P moving along some general path in space. If the particle is confined to a specified path, as with a bead sliding along a fixed wire, its motion is said to be constrained . If there are no physical guides, the motion is said to be unconstrained .
eBook - PDF- Jerry B. Marion(Author)
- 2013(Publication Date)
- Academic Press(Publisher)
C H A P T E R 3 Fundamentals of Newtonian Mechanics 3.1 Introduction The science of mechanics seeks to provide a precise and consistent description of the dynamics of particles and systems of particles. That is, we attempt to discover a set of physical laws which provide us with a method for mathematically describing the motions of bodies and aggre-gates of bodies. In order to do this, we need to introduce certain funda-mental concepts. It is implicit in Newtonian theory that the concept of distance is intuitively understandable from a geometrical viewpoint. Further-more, time is considered to be an absolute quantity, capable of precise definition by an arbitrary observer. In relativity theory, however, we must modify these Newtonian ideas (see Chapter 4). The combination of the concepts of distance and time allows us to define the velocity and accelera-tion of a particle. The third fundamental concept, mass, requires some ela-boration which we shall give in connection with the discussion of Newton's laws. The physical laws which we introduce must be based on experimental fact. A physical law may be characterized by the statement that it might have been otherwise. Thus, there is no a priori reason to expect that the 56 3.2 NEWTON'S LAWS 57 gravitational attraction between two bodies must vary exactly as the inverse square of the distance between them. But experiment indicates that this is so. Once a set of experimental data is correlated and a postulate is formula-ted regarding the phenomena to which the data refer, then various impli-cations can be worked out. If these implications are all verified by experi-ment, there is reason to believe that the postulate is generally true. The postulate then assumes the status of a physical law. If some experiments are found to be in disagreement with the predictions of the law, then the theory must be modified in order to be consistent with all known facts. Newton has provided us with the fundamental laws of mechanics.
eBook - PDFMechanics
Lectures on Theoretical Physics, Vol. 1
- Arnold Sommerfeld(Author)
- 2016(Publication Date)
- Academic Press(Publisher)
CHAPTER I MECHANICS OF A PARTICLE § 1. Newton's Axioms The laws of motion will be introduced in axiomatic form; they summarize in precise form the whole body of experience. First law: Every material body remains in its state of rest or of uniform rectilinear motion unless compelled by forces acting on it to change its state. 1 We shall at first withhold explanation of the concept of force introduced in this law. We notice that the states of rest and of uniform {rectilinear) motion are treated on equal footing and are regarded as natural states of the body. The law postulates a tendency of the body to remain in such a natural state; this tendency is called the inertia of the body. One often speaks of Galileo's law of inertia instead of Newton's first law in referring to the above axiom. We must say in this connection that while it is perfectly true that Galileo arrived at this law long before Newton (as a limiting result of his experiments with sliding bodies on planes of vanishing inclination), we find it characteristic of Newton that the law holds top position in his system. Newton's word body will, for the time being, be replaced by the words particle or mass point. To formulate the first law mathematically we shall make use of definitions 1 and 2 preceding it in the Principia. Definition 2 : The quantity of motion is the measure of the same, arising from the velocity and the quantity of matter conjunctly. 2 The quantity of motion is hence the product of two factors, the velocity, whose meaning is geometrically evident, 3 and the quantity of 1 We mention here, and in connection with what is to follow, the book Die Mechanik in ihrer Entwickelung (8th ed., F. A. Brockhaus, Leipzig, 1923; translated into English under the title The Science of Mechanics, Open Court Publishing Co., LaSalle, 111., 1942) by Ernst Mach.
eBook - PDFMechanics
Lectures on Theoretical Physics
- Arnold Sommerfeld(Author)
- 2013(Publication Date)
- Academic Press(Publisher)
CHAPTER I MECHANICS OF A PARTICLE § 1. Newton's Axioms The laws of motion will be introduced in axiomatic form; they summarize in precise form the whole body of experience. First law : Every material body remains in its state of rest or of uniform rectilinear motion unless compelled by forces acting on it to change its state. 1 We shall at first withhold explanation of the concept of force introduced in this law. We notice that the states of rest and of uniform (rectilinear) motion are treated on equal footing and are regarded as natural states of the body. The law postulates a tendency of the body to remain in such a natural state; this tendency is called the inertia of the body. One often speaks of Galileo's law of inertia instead of Newton's first law in referring to the above axiom. We must say in this connection that while it is perfectly true that Galileo arrived at this law long before Newton (as a limiting result of his experiments with sliding bodies on planes of vanishing inclination), we find it characteristic of Newton that the law holds top position in his system. Newton's word body will, for the time being, be replaced by the words particle or mass point. To formulate the first law mathematically we shall make use of definitions 1 and 2 preceding it in the Principia. Definition 2 : The quantity of motion is the measure of the same, arising from the velocity and the quantity of matter conjunctly. 2 The quantity of motion is hence the product of two factors, the velocity, whose meaning is geometrically evident, 8 and the quantity of 1 We mention here, and in connection with what is to follow, the book Die Mechanik in ihrer Entwickelung (8th ed., F. A. Brockhaus, Leipzig, 1923; translated into English under the title The Science of Mechanics, Open Court Publishing Co., LaSalle, 111., 1942) by Ernst Mach.
eBook - PDF- Delo E. Mook, Thomas Vargish(Authors)
- 2018(Publication Date)
- Princeton University Press(Publisher)
In this book we will attempt to provide clear definitions of such words in the scientific sense, and we will be careful to use them only in that sense. The glossary is provided to help with this. 2.5 N E W T O N ' S SECOND LAW 37 an object's motion is also inherent in a specification of its momentum. Therefore, a change in the momentum of an object may be caused by a change in the object's mass, its speed, or its direction of travel. We will encounter the term mass in a number of contexts in this and later chapters. Each time it will be important that we discuss its specialized meaning in that particular context. Within the context of Newton's second law, mass pertains to the object whose change in motion is being described by the law. It measures the property of the object known as inertia, which, in turn, is a term describing the reluctance an object has to change its state of motion. Later on we will encounter the term mass used to describe something entirely different: the propensity of objects to attract one another through action of the force of gravity. In this gravitational context, mass is related to (but not at all the same as) the weight of an object. For the present, mass should be thought of as the measure of iner-tia—how much opposition a body presents to having its state of motion changed. The momentum is defined by the product of this measure of in-ertia with the speed of the object. In modern terms, then, the second law may be stated as follows: The change in momentum of an object is directly proportional to the size of the force acting on the object, where a change in momentum may be due to a change in the object's mass or to an acceleration of the object or to both an acceleration and a change in mass. It bears repeating at this point that an acceleration includes a change in speed, a change in direction of travel, or a combination of both (figure 2.6).
- Emilie Du Châtelet, Judith P. Zinsser, Isabelle Bour, Judith P. Zinsser(Authors)
- 2009(Publication Date)
- University of Chicago Press(Publisher)
WHAT MUST BE CONSIDER ED IN MOTION. § .230. Several things are considered in motion: 1. The force that imparts the motion to the body. 2. The time during which the body moves. 3. The space the body traverses. 4. The speed of motion, this is to say, the relationship between the space the body has traversed and the time used to traverse it. 5. The mass of the bodies, according to which they resist the force that wants to impart or to take away motion from them. 6. The quantity of motion. 7. The direction of motion, be it simple or compound. 8. The elasticity of the bodies to which the motion is imparted. 9. The effect of the force of the moving bodies, or the quantity of ob-stacles that they can disrupt in consuming their force. 104 10. Finally, the way in which the motion is communicated. § .231. There is no motion without a force that imparts it. 1. OF MOTOR FORCE . The active cause that imparts the motion to the body, or which incites it to move, is called motor force. The effect of this force, when it is not destroyed by an invincible re-sistance, is to make the body traverse a certain space, in a certain time, in a space that does not perceptibly resist; and in a space that resists, its effect is to make it overcome some of the obstacles it encounters. This cause, which draws the stationary body from the state of rest it was in, and which makes it traverse a certain space and overcome a certain quantity of obstacles, communicates to this body a force that it did not have when at rest, since according to the First Law, the body by itself would never leave its place. § .232. By the same Law, when a moving body ceases moving, some 104. Du Châtelet here enunciates Johann Bernoulli’s and Leibniz’s ideas, that a body’s mo-tion can be understood and calculated by “obstacles overcome.” See also her section on “motor force,” §§ .234–35, and § .268. Foundations of Physics 179 force equal and opposite to its own must have stopped its motion and con-sumed its force.
eBook - PDFApplied Mathematics
Made Simple
- Patrick Murphy(Author)
- 2014(Publication Date)
- Butterworth-Heinemann(Publisher)
If a boy runs forward with a velocity ν carrying a plastic windmill of mass m, the linear momentum of the windmill is mv regardless of the direction in which the windmill is rotating about its centre. Since linear momentum is the product of a mass (kilogrammes) and a velocity (metres per second), it follows that the unit of momentum is kilo-gramme metre per second (abbreviated to k g m s 1 ) . For example, if each wheel of a car has a mass of 10 kg, the momentum of each wheel when the car is travelling with a velocity of 15 m s 1 is 150 kg m s 1 . If the total mass of the car and occupants is 1000 kg, the momentum of the car and occupants is 15000 k g m s -1 . Newton's Laws of Motion may be stated as follows: 1. Every body will continue in a state of rest or uniform motion in a straight line unless acted upon by an external applied force. 2. The rate of change of motion is proportional to the applied force and takes place in the direction of that force. 3. T o each action there is an equal and opposite reaction. The third law has already been discussed in Chapter One (page 9). It is not possible to give a proof of these laws, but there is a great deal of experimental evidence for assuming their truth. The assumption that the laws are true is borne out by the fact that the motions of the stars and planets have been, and are, computed with a high degree of accuracy which is constantly confirmed by astronomical observations. The time and place of eclipses and tides throughout the world are all officially noted and predicted in the Nautical Almanac; again the overall accuracy of the forecasts convinces us that the laws are valid for all such practical purposes. (2) The First Law The first law provides the definition of force which we have already quoted in Chapter One: 'force is that which tends to change the state of rest or uniform motion of a body'. It should be noted that it is the resultant force on the body which is being discussed in each case.
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