Physics
Position and Displacement
Position refers to the location of an object in space, often described using coordinates. Displacement, on the other hand, is a vector quantity that measures the change in position of an object, taking into account both the magnitude and direction of the change. It is the shortest distance between the initial and final positions of the object.
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7 Key excerpts on "Position and Displacement"
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
67 4.1 Position and Displacement Learning Objectives After reading this module, you should be able to . . . 4.1.1 Draw two-dimensional and three-dimensional position vectors for a particle, indicating the components along the axes of a coordinate system. 4.1.2 On a coordinate system, determine the direction and magnitude of a particle’s position vector from its components, and vice versa. 4.1.3 Apply the relationship between a particle’s dis- placement vector and its initial and final position vectors. Key Ideas ● The location of a particle relative to the origin of a coordinate system is given by a position vector r → , which in unit-vector notation is r → = x ˆ i + y ˆ j + z k ̂ . Here x ˆ i, y ˆ j, and z k ̂ are the vector components of posi- tion vector r → , and x, y, and z are its scalar components (as well as the coordinates of the particle). ● A position vector is described either by a magnitude and one or two angles for orientation, or by its vector or scalar components. ● If a particle moves so that its position vector changes from r → 1 to r → 2 , the particle’s displacement Δ r → is Δ r → = r → 2 − r → 1 . The displacement can also be written as Δ r → = ( x 2 − x 1 ) ˆ i + ( y 2 − y 1 ) ˆ j + ( z 2 − z 1 )k ̂ = Δx ˆ i + Δy ˆ j + Δz k ̂ . What Is Physics? In this chapter we continue looking at the aspect of physics that analyzes motion, but now the motion can be in two or three dimensions. For example, medical researchers and aeronautical engineers might concentrate on the physics of the two- and three-dimensional turns taken by fighter pilots in dogfights because a modern high-performance jet can take a tight turn so quickly that the pilot immediately loses consciousness. A sports engineer might focus on the physics of basketball. For example, in a free throw (where a player gets an uncontested shot at the basket from about 4.3 m), a player might employ the overhand push shot, in which the ball is pushed away from about shoulder height and then released.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
62 C H A P T E R 4 Motion in Two and Three Dimensions 4-1 Position and Displacement Learning Objectives After reading this module, you should be able to . . . 4.01 Draw two-dimensional and three-dimensional posi- tion vectors for a particle, indicating the components along the axes of a coordinate system. 4.02 On a coordinate system, determine the direction Key Ideas ● The location of a particle relative to the origin of a coordinate system is given by a position vector r → , which in unit-vector notation is r → = xi ˆ + yj ˆ + zk ˆ . Here xi ˆ , y j ˆ , and zk ˆ are the vector components of position vector r → , and x, y, and z are its scalar components (as well as the coordinates of the particle). ● A position vector is described either by a magnitude What Is Physics? In this chapter we continue looking at the aspect of physics that analyzes motion, but now the motion can be in two or three dimensions. For example, medical researchers and aeronautical engineers might concentrate on the physics of the two- and three-dimensional turns taken by fighter pilots in dogfights because a modern high-performance jet can take a tight turn so quickly that the pilot immediately loses consciousness. A sports engineer might focus on the physics of basketball. For example, in a free throw (where a player gets an uncontested shot at the basket from about 4.3 m), a player might employ the overhand push shot, in which the ball is pushed away from about shoulder height and then released. Or the player might use an underhand loop shot, in which the ball is brought upward from about the belt-line level and released. The first technique is the overwhelm- ing choice among professional players, but the legendary Rick Barry set the record for free-throw shooting with the underhand technique. Motion in three dimensions is not easy to understand.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
C H A P T E R 4 Motion in Two and Three Dimensions 4-1 Position and Displacement Learning Objectives After reading this module, you should be able to . . . 4.01 Draw two-dimensional and three-dimensional posi- tion vectors for a particle, indicating the components along the axes of a coordinate system. 4.02 On a coordinate system, determine the direction Key Ideas ● The location of a particle relative to the origin of a coordinate system is given by a position vector r → , which in unit-vector notation is r → = xi ˆ + yj ˆ + zk ˆ . Here xi ˆ , y j ˆ , and zk ˆ are the vector components of position vector r → , and x, y, and z are its scalar components (as well as the coordinates of the particle). ● A position vector is described either by a magnitude What Is Physics? In this chapter we continue looking at the aspect of physics that analyzes motion, but now the motion can be in two or three dimensions. For example, medical researchers and aeronautical engineers might concentrate on the physics of the two- and three-dimensional turns taken by fighter pilots in dogfights because a modern high-performance jet can take a tight turn so quickly that the pilot immediately loses consciousness. A sports engineer might focus on the physics of basketball. For example, in a free throw (where a player gets an uncontested shot at the basket from about 4.3 m), a player might employ the overhand push shot, in which the ball is pushed away from about shoulder height and then released. Or the player might use an underhand loop shot, in which the ball is brought upward from about the belt-line level and released. The first technique is the overwhelm- ing choice among professional players, but the legendary Rick Barry set the record for free-throw shooting with the underhand technique. Motion in three dimensions is not easy to understand.
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 - PDFFrom Atoms to Galaxies
A Conceptual Physics Approach to Scientific Awareness
- Sadri Hassani(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
Chapter 6 Kinematics: Describing Motion Chapter 4 taught us some basic knowledge of motion along a straight line. This chapter generalizes the concept of motion and introduces some fundamental quantities necessary for its description. 6.1 Position, Displacement, and Distance What is motion? Vaguely speaking, it is the change in the state of an object. More precisely, it is the change in the position of an object with time. Still more precisely, we must speak of the motion of an object relative to an observer , although the “object” could be a person, and the “observer” a thing. To analyze the motion, draw an arrow from the “observer” O to the “object” A , and call the arrow the position vector . 1 The very definition of the position vector assumes Position vector. that both O and A are points. The position vector, denoted commonly by r , determines the instantaneous position of the object A [Figure 6.1(a)] relative to an observer O . The word “instantaneous” is important because the position of the point object A is, in general, constantly changing. If we were to take snapshots of A at various times, t 1 , t 2 , t 3 , etc., and label the corresponding points at which A is located by A 1 , A 2 , A 3 , etc, we would have a situation depicted in Figure 6.1(b), with position vectors r 1 , r 2 , r 3 , etc. In this figure, only three out of an infinitude of possible snapshots are shown. Bear in mind that every directed line segment from O to a point on the curve in Figure 6.1 is a possible position vector. What do you know? 6.1. Can you say that the observer—as defined in the descrip-tion of motion—does not move? If the point A does not change, i.e., if the position vector r does not vary with time, we say that the object is stationary relative to O . You have to make a clear distinction between the distance between O and A , which is the length of r , and the position vector, which is the directed line segment r .
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Here in Chapter 2, we begin the study of mechanics—the study of how objects move in response to forces. Before we consider forces, though, we will learn to simply describe motion, which is the subject of kinematics. Chapter 2 deals exclusively with one- dimensional kinematics, which is most simply defined as motion along a straight line. Pictured here is the Drop Tower thrill-ride found at Kings Dominion amusement park in Richmond, Virginia. It is the largest of its kind, with an overall height of 93 m, a drop distance of 83 m, and a maximum speed of 116 km/h. It dramatically illustrates motion along a straight line. Joel Bullock (TheCoasterCritic.com) 2 Kinematics in One Dimension 42 Position and Displacement: Vectors in One Dimension | 43 2.1 Calculate the distance and displacement when an object moves from place to place. 2.1.1 Match a vector sum to a diagram representing the graphical sum of those vectors. The world around us moves. Some motion is slow and steady, like the motion of the pas- sengers on a slow-moving escalator. Some motion is fast and unsteady, like the motion of a zigzagging gazelle being chased by a cheetah. Describing motion is the subject of kinematics, which brings together the ideas of distance and time to form the various quan- tities that are required for a complete description of motion. Here in Chapter 2 we focus on one-dimensional motion—the simplest case. Understanding motion is a prerequisite for many topics in this text, such as the conservation of energy, thermodynamics, and special relativity. Position When specifying the position of an object, there is some uncertainty based on the object’s finite size. An automobile, for example, is about 5 m long, 2 m wide, and 2 m high, and it can assume a variety of orientations—facing north, south, and so on. Specifying a single point in space to be the “location” of the car introduces some uncertainties.
eBook - PDF- John Matolyak, Ajawad Haija(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
25 © 2010 Taylor & Francis Group, LLC Motion in One Dimension This chapter addresses deriving and using the equations of motion that describe the time depen-dence of an object’s displacement, velocity, and acceleration. Relationships between displacement, velocity, and acceleration are also of importance and will be derived. This chapter starts with the basic definitions of displacement and average velocity of an object moving in one dimension. Such a simplified start will help to lead a complete set of equations of motion for an object moving along one dimension, east–west, north–south, or up and down. In the context of coordinate systems that were treated in the previous chapter, the one-dimensional motion will reduce the time and effort needed on the study of motion in two dimensions, which is the subject of the next chapter. 2.1 DISPLACEMENT Motion can be defined as a continuous change in position and that change could occur in one, two, or three dimensions. As the treatment here will be limited to motions only in one dimension, one axis of the coordinate system described in Chapter 1 will suffice. Choosing this axis as the x-axis, we depict on it a point, O, which will be considered as an origin of zero coordinate. Any point on the right of the origin O will have a positive coordinate and any point on the left of O will have a negative coordinate (Figure 2.1). The displacement, denoted by Δ x, of an object as it moves from an initial position x i to a final position x f along the x-axis can be defined as the change in the object’s position along the x-axis. That is Δ x = x f – x i . (2.1) 2.1.1 S PECIAL R EMARKS The quantities in Equation 2.1 are treated as vectors. x i is the initial position vector, x f the final posi-tion vector, and Δ x the displacement vector. Accordingly, all these quantities have a direction and magnitude.
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