12 - Kinematics of a Particle

12.1 Introduction
12.2 Rectilinear Kinematics : Continuous Motion
12.3 rectilinear Kinematics : Erratic Motion
12.4 General Curvilinear Motion
12.5 Curvilinear Motion : Rectilinear Components
12.6 Motion of a Projectile
12.7 Curvilinear Motion : Normal and Tangential Components
12.8 Curvilinear Motion : Cylindrial
12.9 Absolute Dependent Motion Analysis of Two Particles
12.10 Relative-Motion of Two Particles Using Translating Axes

Chapter Objectives

To introduce the concepts of position, displacement, velocity, and acceleration.
To study particle motion along a straight line and represent this motion graphically.
To investigate particle along a curved path using different coordinate systems.
To present an analysis of dependent motion of two particles.
To examine the priciples of relative motion of two particles using translating axes.

12.1 Introduction

Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies subjected to the action of forces. Engineering mechanics is divided into two areas of study, namely, statics and dynamics. Statics is concerned with the equilibrium of a body that is either at rest or moves with constant velocity. Here we will consider dynamics, which deals with the accelerated motion of a body. The subject of dynamics will be presented in two parts : kinematics, which treats only the geometric aspects of the motion, and kinetics, which is the analysis of the forces causing the motion. To develop these principles, the dynamics of a particle will be discussed first, followed by optics in rigid-body dynamics in two and then three dimensions.

Historically, the principles of dynamics developed when it was possible to make an an accurate measurement of time. Galileo Galilei (1564-1642) was one of the first major contributors to this field. His work considered of experiments using pendulums and falling bodies. The most significant contributions in dynamics, however, were made by Issac Newton (1642-1727), who is noted for his formulation of the three fundamental laws of motion and the law of universal
gravitational attraction. Shortly after these laws were postulated, important techniques for their application were developed by Euler, D'Alember,Lagrange, and others.

There are many problems in engineering whose solutions require application of the principles of dynamics. Typically the structural design of any vehicle, such as an automobile or airplane, requrires consideration of the motion to which it is subjected.

Problem Solving :

Dynamics is considered to be more involed than statics since both the forces applied to a body and its motion must be taken into account. Also, many applications require using calculus, rather than just algebra and trigonometry. In any case, the most effective way of learning the principles of dynamics is to solve problems.

1. Read the problem carefully and try to correlate the actual physical situation with the theory you have studied.
2. Draw any necessary diagrams and tabulate the problem data.
3. Establish a coordinate system and apply the revelant principles, generally in methematical form.
4. Solve the necessary equations algebraically as far as practical; then, use a consistent set of units and complete the solution numerically. Report the answer with no more significant figures than the accurancy of the given data.
5. Study the answer using technical judgement and common sense to determine whether or not it seems reasonable.
6. Once the solution has been completed, revier the problem. Try to think of other ways of obtaining the same solution.

12.2 Rectilinear Kinematics : Continuous Motion
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