Technology & Engineering
Rectilinear Kinematics
Rectilinear kinematics is a branch of mechanics that deals with the motion of objects in a straight line. It involves the study of displacement, velocity, and acceleration of objects moving in a straight line without considering the forces that cause the motion. Rectilinear kinematics is used in various fields, including physics, engineering, and robotics.
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5 Key excerpts on "Rectilinear Kinematics"
eBook - PDF- Richard C. Hill, Kirstie Plantenberg(Authors)
- 2013(Publication Date)
- SDC Publications(Publisher)
14 2.2.5) Constant acceleration equations ....................................................................... 15 2.2.6) General notes .................................................................................................... 16 2.3) ERRATIC RECTILINEAR MOTION......................................................................... 25 2.4) SOLVING RECTILINEAR PROBLEMS GRAPHICALLY ....................................... 32 CHAPTER 2 REVIEW PROBLEMS ............................................................................... 37 CHAPTER 2 PROBLEMS .............................................................................................. 41 CHAPTER 2 COMPUTER PROBLEMS ......................................................................... 48 CHAPTER 2 DESIGN PROBLEMS ................................................................................ 49 CHAPTER 2 ACTIVITIES ............................................................................................... 49 Conceptual Dynamics Kinematics: Chapter 2 – Kinematics of Particles - Rectilinear Motion 2 - 2 CHAPTER SUMMARY In this chapter, we will study kinematics of particles. Kinematics involves the study of a body's motion without regard to the forces that generate that motion. In particular, kinematics involves studying the relationship between displacement, velocity and acceleration. This chapter will focus on analyzing simple one-dimensional motion. The next chapter will move on to more complex two-dimensional motion. The treatment of particles precedes rigid bodies because they are simpler to analyze. A particle may be treated as a point; it has mass but no size. Therefore, we will only need to consider translational motion and not worry about rotation. Conceptual Dynamics Kinematics: Chapter 2 – Kinematics of Particles - Rectilinear Motion 2 - 3 2.1) RECTILINEAR MOTION 2.1.1) RECTILINEAR MOTION The motion of a real object with size and mass is very complex.
eBook - PDF- Carl T. F. Ross(Author)
- 1997(Publication Date)
- Woodhead Publishing(Publisher)
CHAPTER TWO Kinematics of Particles 2.1 INTRODUCTION This chapter is divided into two sections, one section is on rectilinear motion and the other section is on plane curvilinear motion. Now rectilinear motion can be described as one dimensional motion or motion in a straight line. The section on rectilinear motion is sub-divided into two sub-sections, namely motion when the acceleration is constant and motion when the acceleration varies with time or distance or velocity. The section on plane curvilinear motion is divided into three sub-sections. One of these sub-sections is on plane motion with reference to the rectangular axes, namely x and y, while another sub-section is on plane motion with reference to the normal and tangential axes of the path of the motion. These axes are often called the not axes, where 'n' is perpendicular to the path of the motion and 't' is tangential to the path of the motion. Thus, if the path of the motion is curvilinear, the directions of 'n' and 't' will vary. The third sub-section on plane motion is on motion in terms of the polar co-ordinates 'r' and '8', where 'r' is radially outwards and '8' is tangential to 'r', in an angular direction. The x-y rectangular co-ordinate system is popular when the motion or its direction is known in terms of the x-y co-ordinates. The not co-ordinate system is popular when the direction of the path that the motion follows is known. This may be in the case of a car or a train travelling around a curve, whose equation is known. Polar co-ordinates are popular for analysing mechanisms and other artefacts, which are rotating about a fixed point. Also considered in this chapter is relative motion of translating axes and the motion of connected particles. 2.2 RECTILINEAR MOTION Rectilinear motion of a particle can be described as motion in a straight line, as shown by Figure 2.1, where the particle 'P' moves to the position 'ph in time'!1t'.
eBook - PDFEngineering Mechanics
Problems and Solutions
- Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
1 2 3 4 B A Fig. 10.1 500 Engineering Mechanics The average acceleration is defined as the ratio of average velocity to the time internal Δ t and expressed as a v t avg avg = ∆ The instantaneous acceleration is defined as the ratio of instantaneous velocity to the time interval Δ t and expressed as lim . t inst velocity v t dv dt → 0 ∆ or 10.3 Rectilinear Motion During motion, a particle can have three types of motion i.e., translational, rotational or general plane motion. In this chapter, we will study translational motion. Rotational motion and general plane motion are discussed in chapter 15. In translational motion, the particle travels along a straight line path without rotation; it is also known as rectilinear motion. In this type of motion, all particles of a body travel along a straight line only i.e., bears only one dimensional motion. The rectilinear motion may lie along X-axis or Y-axis. The examples of rectilinear motion along X-axis are motion of vehicles on a straight track (road without speed breaker), motion of piston in a horizontal cylinder. However, the motion of lift in a building and falling of a stone vertically are examples of rectilinear motion along Y-axis. 10.4 Rectilinear Motion in Horizontal Direction (X-axis) A particle moving in a straight line can have either uniform or variable acceleration. Generally the particles consist of variable acceleration in actual practice. The motion of a body under variable acceleration can be analyzed by using differential and integral equations of motion. The motion under uniform acceleration is analyzed by using equations of motion as discussed in next section (10.4.2). 10.4.1 Motion with variable acceleration Differential equations of motion: These equations are used to analyze the motion of a body having variable acceleration. The equations for four parameters of motion i.e., displacement, time, velocity and acceleration are given by v dx dt a dv dt d x dt v dv dx = = or or 2 2
- H. D. Ram, A. K. Chauhan(Authors)
- 2015(Publication Date)
- Cambridge University Press(Publisher)
6 KINEMATICS OF PARTICLE AND RIGID BODY 6.1 Introduction Kinematics is the study of the motion of particles and rigid bodies disregarding the forces associated with these motions. 6.2 Kinematics of particle Kinematics of particle involves the study of position, velocity and acceleration of the particle without any consideration of the forces working on it. Particle can move on a straight line, on a plane or in space. We will restrict our study to plane motion only. The plane motion of the particle is classified as: (a) Straight line motion (b) Motion on curved path Following classification of motion on curved path is useful from application point of view (a) Position, velocity and acceleration in terms of Cartesian components (b) Position, velocity and acceleration in terms of path variables and (c) Position, velocity and acceleration in terms of polar coordinates 6.3 Straight line motion of particle The rectilinear motion of particle is the motion along straight line. Suppose a point is moving along x-axis, The position of the particle at time t is x The position of the particle at time ( t + t ) is ( x + x ). The displacement of the particle during the time interval t is equal to {( x + x ) – x or x } The average velocity of the particle, Kinematics of Particle and Rigid Body | 341 v x t av = Δ Δ Instantaneous velocity of the particle is the limiting value of average velocity as time t → 0. Therefore, v x t t = → lim Δ Δ Δ 0 or, v dx dt = (6.1) Suppose the velocity of the particle at time t is v and at time ( t + t ) its velocity is ( v + v ). Average acceleration is given by: a v t av = Δ Δ Instantaneous acceleration of the particle is the limiting value of average acceleration as time Δ t → 0 . Therefore, a v t t = → lim Δ Δ Δ 0 or, a dv dt = (6.2) Rectilinear motion of the particle with constant acceleration a : Suppose a particle is moving along x-axis. At t = 0, the position is x 0 and the velocity is v 0 .
eBook - PDFMechanotechnics N6 Student's Book
TVET FIRST
- Sparrow Consulting(Author)
- 2021(Publication Date)
- Macmillan(Publisher)
196 Module 8 TVET FIRST Figure 8.1: Examples of motion In this module, you will learn about the study of motion called kinematics. This describes the way objects move without considering the forces responsible for the motion. The module focuses on the motion of kinematic links and chains. These are the moving parts of mechanisms that are found in machines. Starter activity Discuss the following in class: 1. Consider examples of machines such as a lathe, robotic arm or internal combustion engine. Which parts are in motion and which are stationary? Why is it necessary to have both stationary and moving parts? 2. Imagine being inside a moving elevator, vehicle, bus or spaceship. How would objects outside look if they are moving from your position? How would fellow passengers or other objects inside be moving? Discuss how different reference frames affect how you describe the motion of an object. 3. Think of examples where angular motion is converted to linear motion or linear motion to angular. (Hint: Angular motion refers to rotation, while linear motion is in a straight line.) Unit 8.1: Motion All objects and physical processes move. Examples include a book falling off a table, a person walking on a pavement, a fish swimming, air flowing in and out of your lungs, and so on. Motion, therefore, refers to a change in the position of an object with respect to time. As soon as there is a change in the distance between two objects, they move in relation to each other. 8.1.1 Relative motion, velocity and acceleration Relative motion How do you know that something is moving? The location of any object at any particular time is its position. This position Note If a straight line between two objects changes in direction or length, motion is taking place. One object moves in relation to the other. reference frame: a reference point (point of origin) combined with a set of directions
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