Physics
Kinematics Physics
Kinematics in physics is the study of motion, focusing on the position, velocity, and acceleration of objects without considering the forces causing the motion. It involves analyzing the motion of objects using mathematical equations and graphs to describe their movement. Kinematics provides a foundation for understanding more complex concepts in physics, such as dynamics and energy.
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10 Key excerpts on "Kinematics Physics"
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 .
- 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- Bogdan Skalmierski(Author)
- 2013(Publication Date)
- Elsevier(Publisher)
CHAPTER 1 Kinematics The primary concepts in mechanics are space and time. Regarding space, we shall assume that it is Euclidean (plane), therefore an orthogonal frame of reference can be applied to it. Furthermore, it will be assumed that space is uniform and isotropic, i.e., there are no distinct loci nor preferred directions in it. With regard to time, it will be recognized as uniform, i.e., preferred instants are non-existent in it. Some parts of this book deal with problems within the purview of classical mechanics, therefore the following two hypotheses have been accepted: 1. Time is absolute, i.e. it runs identically in all frames of reference (moving and fixed). 2. The distance between two arbitrary points in space, irrespective of the frame of reference in which it is measured, is identical (it is an invariant). Kinematics is a science of motion but it is not concerned with the causes liable to induce or disturb motion. By motion we shall understand changes in time in the position of a body referred to a system treated as stationary. The position of a body or configuration is an area of Euclidean space, in which the particles of that body have been mapped one-to-one and continuously. This mapping we shall call homeomorphism. Accordingly, motion is the change of mapping in time. Note that the concept of motion is relative, since it depends on the adopted frame of reference. 1.1 Motion of a single particle We assume a right-handed frame of reference Oxyz in a space (Fig. 1.1), embracing a triplet of unit vectors, i, j, and k, which correspond to x, y, Fig. 1.1 12 KINEMATICS Ch. 1 and z. In a space endowed with such orientation we shall consider the motion of a single particle determined by a position vector r(t). This vector, being the function of time t, can be written as follows: r(t) = x(t)i+y(t)j+z(t)k (1) or more concisely, using the summation convention, r(t) = x`(t)e i .
Available until 25 Jan |Learn more- Tai L. Chow(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
Also, the new frontiers of nonlinear behavior— chaos and stochastic motion—are analyzed using classical mechanics. A good grasp of classical mechanics is therefore a prerequisite for the study of the new theories of physics. This chapter will survey a number of fundamental concepts, such as velocity and accelera-tion, which are basic to our presentation in the succeeding chapters. The branch of mechanics that describes motion that does not require knowledge of its cause is called “kinematics,” and the part of mechanics that concerns the physical mechanisms that cause the motion to take place is termed “dynamics.” We shall mainly be concerned with particle dynamics; the motion of rigid bodies will be addressed in Chapter 12. A body has both mass and extent, and a particle is a body whose dimen-sions may be neglected in describing its motion. Whether we can treat the motion of a given body as that of a particle depends not only on its size but also on the conditions of the physical problem concerned. The Earth may be regarded as a particle in the context of its motion around the sun but not in a discussion of its daily rotation on its axis. 1.2 SPACE, TIME, AND COORDINATE SYSTEMS Motion involves the change in the body’s position in space as time progresses. So we shall develop classical mechanics in terms of certain notions of space and time. We shall not go into a deep philo-sophical discussion on the basic concept of space and time that is a very difficult one to comprehend or described at our level. We are concerned with the motion of bodies, and so it is only necessary for a concept of space to provide a way in which the position of such bodies can be described. We may regard space, in classical mechanics, simply as the set of possible positions that the component points of a body may occupy. Because position of a point can only be defined relative to a set of other points, position is, therefore, a relative concept.
No longer available |Learn more- Ping YI, Jun LIU, Feng JIANG(Authors)
- 2022(Publication Date)
- EDP Sciences(Publisher)
Chapter 6 Kinematics of Particles Objectives Understand the kinematic concepts of position, displacement, velocity, and acceleration. Investigate a particle’s curvilinear motion using different coordinate systems. Study absolute dependent motion of two particles. Analyze relative motion of two particles using a translating coordinate system. Statics deals with forces that lead to equilibrium of particles or bodies. However, kinematics cares about only the geometrical aspects of the motion, such as position, displacement, velocity and acceleration, without involving forces. The analysis object in kinematics can also be considered as a particle or a rigid body. If the motion analyzed is characterized by the motion of the object’s mass center and the dimensions (size and shape) have no or little influence on the motion, this object can be considered as a particle. For example, when we analyze a plane’s trajectory or its position as a function of time, figure 6.1, it can be considered as a particle although it is not small at all to our naked eyes. But if we analyze the fighter plane’s rotation and flipping, figure 6.2, it has to be considered as a body since the dimensions influence the motion greatly. So, we can see that whether an object can be considered as a particle or not is decided by its motion analysis, not by its physical dimensions. Following the cognitive process of learning from the simple to the complex, this chapter considers the motion of a particle, and the motion of a rigid body will be discussed in the next chapter. DOI: 10.1051/978-2-7598-2901-9.c006 © Science Press, EDP Sciences, 2022 6.1 General Curvilinear Motion When a particle moves along a straight line, it undergoes rectilinear motion; whereas a particle moving along a curved path undergoes curvilinear motion. Rectilinear motion has been considered extensively in physics and it will be treated as a special case of curvilinear motion.
- Paul Anthony Russell(Author)
- 2021(Publication Date)
- Reeds(Publisher)
The study of kinematics concentrates on describing motion in words, numbers, diagrams, graphs, and equations. These help the engineer develop cognitive understanding about the way objects behave in the material world. The abstract realism will not be divorced from the object and forces involved; although these are Kinematics • 51 not part of the discipline, some reference to force and objects does help in shaping the engineer’s thought processes. Case A represents a body that was moving at 5 m/s due east, having its velocity changed to 12 m/s due east; the vector of each velocity is drawn from a common point; the difference between the free ends of the vectors is the change of velocity – in this case it is 7 m/s. Case B is a body with an initial velocity of 9 m/s due east, being changed to 2 m/s due west; the vector diagram shows the vector of each velocity drawn from a common point; the difference between their free ends is the change of velocity, which is 11 m/s. Case C is that of a body with an initial velocity of 6 m/s due east changed to 8 m/s due south. The vector diagram is constructed on the same principle of the two vectors drawn from a common point. The change of velocity is, as always, the difference between the free ends of the two vectors, this is, 8 6 10 2 2 + = m/s. The direction for change of velocity is S 36° 52’ W due to change in velocity taking place in the direction of the applied force, which in this case is east to south-west. In all cases, the vector diagrams are constructed by drawing the velocity vectors from a common point. This technique is called vector subtraction. Space diagrams Vector diagrams A 5 m/s 9 m/s 2 m/s 6 m/s 8 m/s 12 m/s B C N S 5 7 12 W E 9 6 8 Change of velocity 11 2 ▲ Figure 2.10 Space and vector diagrams for a change in velocity 52 • Applied Mechanics Acceleration is the rate of change of velocity; therefore, in all of these cases the value of acceleration can be obtained by dividing change of velocity by time.
eBook - PDF- David Agmon, Paul Gluck;;;(Authors)
- 2009(Publication Date)
- WSPC(Publisher)
Chapter 2 Kinematics All is influx, nothing stands still. Heraclitus Kinematics is a part of mechanics dealing with the description of motion and the functional relationships between a body's position, velocity, acceleration and time. Complex objects like a car or an airplane are treated as if they were a single mass point, called a particle, allowing one to ignore internal motions. This greatly simplifies the description of the position and related quantities. 2.1 Position and displacement Position is specified with respect to some arbitrary coordinate system, the latter always chosen to satisfy the need for convenience and simplicity. It is usual y { to work with three mutually perpendicular (Cartesian) system of axes, x,y£. For motion in a plane or along a line, two axes (x,y) or one axis (usually x) will suffice, respectively. The choice of the origin O is also a matter of convenience. The same spatial point will have different coordinates in different coordinate systems. We shall usually restrict our discussion to motion in a plane, generalization to three dimensions will be simple. The position of a point P with respect to the (x,y)-axes in the diagram may be specified in three different ways: (a) By the pair of numbers (xi,yi)» which represent the projections of the vector r on the x and y axes, respectively. (b) By the pair (r,#), where r is the distance of P from the origin and 6 is the angle between the x-axis and the line OP. (c) By the vector r, with tail at O and tip at P. The dotted line in the diagram is the time-dependent path of a particle. At time t the particle is at P located by the (position) vector /i, at a later time t 2 it is at P 2 given by the vector r 2 . The displacement vector r 2 starts from Pi and ends at P 2 , and is given by r 2 i=r 2 -r 1 as shown. We denote r 21 by Ar . Pi ^21=^2-^1 25
eBook - PDF- Patrick Hamill(Author)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
2 Kinematics Recall that kinematics is the study of motion and, specifically, it is the study of the relationships between position, velocity, acceleration, and time. Kinematics in one dimension is fairly simple because position, velocity, and acceleration can be treated as scalars. Motion in a straight line and rotation about a fixed axis are examples of one-dimensional motion. 1 Some two-dimensional problems, such as the motion of a projectile, can be resolved into two linked one-dimensional problems. However, in general, motion in two or three dimensions complicates the problem significantly because then you need to express the basic quantities as vectors. In this chapter you will learn the relations between the position, velocity, and acceleration in the three main coordinate systems used in physics: Cartesian coordinates, cylindrical coordinates, and spherical coordinates. Although some of the material presented in this chapter will be familiar to you, you will also find many new concepts. These concepts are used throughout the course, so please make sure you understand this chapter thoroughly. Be aware that many students find this material rather difficult. I think it is important for you as a physicist to know something about the people upon whose shoulders you are standing, so in this book I have included a few sections marked “Historical Note.” You will encounter very little physics in these sections, but you might find them interesting and helpful in placing a few famous physicists in historical context. The first historical note describes the life of the person who invented your profession. 2.1 Galileo Galilei (Historical Note) Galileo Galilei (1564–1642) was a brilliant but difficult man whose studies of the physical world launched a scientific and cultural revolution. This cantankerous Italian genius was the first modern scientist. He rejected authority and based his conclusions on observation, experiment, and rational analysis.
eBook - PDF- Harold Josephs, Ronald Huston(Authors)
- 2002(Publication Date)
- CRC Press(Publisher)
57 3 Kinematics of a Particle 3.1 Introduction Kinematics is a study of motion without regard to the cause of the motion. Often this motion occurs in three dimensions. For such cases, and even when the motion is restricted to two dimensions, it is convenient to describe the motion using vector quantities. Indeed, the principal kinematic quantities of position, velocity, and acceleration are vector quantities. In this chapter, we will study the kinematics of particles. We will think of a “particle” as an object that is sufficiently small that it can be identified by and represented by a point. Hence, we can study the kinematics of particles by studying the movement of points. In the next chapter, we will extend our study to rigid bodies and will think of a rigid body as being simply a collection of particles. We begin our study with a discussion of vector differentiation. 3.2 Vector Differentiation Consider a vector V whose characteristics (magnitude and direction) are dependent upon a parameter t (time). Let the functional dependence of V on t be expressed as: (3.2.1) Then, as with scalar functions, the derivative of V with respect to t is defined as: (3.2.2) The manner in which V depends upon t depends in turn upon the reference frame in which V is observed. For example, if V is fixed in a reference frame ˆ R, then in ˆ R, V is independent of t . If, however, ˆ R moves relative to a second reference frame, R, then in R V depends upon t (time). Hence, even though the rate of change of V relative to an observer in ˆ R is zero, the rate of change of V relative to an observer in R is not necessarily zero. Therefore, in general, the derivative of a vector function will depend upon the reference frame in which that derivative is calculated. Hence, to avoid ambiguity, a super-script is usually added to the derivative symbol to designate the reference frame in which V V = ( ) t d dt t t t t t V V V = + ( ) − ( ) → D Lim ∆ ∆ ∆ 0
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
CHAPTER 2 Kinematics in one dimension LEARNING OBJECTIVES After reading this module, you should be able to: 2.1 define one‐dimensional displacement 2.2 discriminate between speed and velocity 2.3 define one‐dimensional acceleration 2.4 use one‐dimensional kinematic equations to predict future or past values of variables 2.5 solve one‐dimensional kinematic problems 2.6 solve one‐dimensional free‐fall problems 2.7 predict kinematic quantities using graphical analysis. INTRODUCTION Australia holds the world record for the longest section of straight railway track: 478 kilometres of the Trans- Australian Railway that traverses the Nullarbor Plain between Sydney and Perth without a single curve. Drivers must stay vigilant for wandering kangaroos and camels as they speed across the endless kilometres of dead straight track, pressing a red ‘dead man’ switch every minute or so for safety. In this chapter we take a look at the properties of straight-line motion, such as displacement, velocity and acceleration. 1 2.1 Displacement LEARNING OBJECTIVE 2.1 Define one-dimensional displacement. There are two aspects to any motion. In a purely descriptive sense, there is the movement itself. Is it rapid or slow, for instance? Then, there is the issue of what causes the motion or what changes it, which requires that forces be considered. Kinematics deals with the concepts that are needed to describe motion, without any reference to forces. The present chapter discusses these concepts as they apply to motion in one dimension, and the next chapter treats two‐dimensional motion. Dynamics deals with the effect that forces have on motion, a topic that is considered in chapter 4. Together, kinematics and dynamics form the branch of physics known as mechanics. We turn now to the first of the kinematics concepts to be discussed, which is displacement. FIGURE 2.1 The displacement Δ x is a vector that points from the initial position x 0 to the final position x.
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