Chapter_12_mod

# Chapter_12_mod - Chapter12:Kinematicsofa Particle...

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1 Chapter 12: Kinematics of a Particle Chapter 12 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 motion along a curved path using different coordinate systems To present an analysis of dependent motion of two particles To examine the principles of relative motion of two particles using translating axes

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2 12.1 Introduction Mechanics: is a branch of physical sciences that is concerned with the state of rest or motion of bodies subjected to the action of forces. This is divided into Statics: concerned with the equilibrium of a body (rest or constant velocity) Dynamics: accelerated motion of a body Dynamics The subject of dynamics will be presented in two parts Kinematics: concerned with only the geometric aspects of the motion Kinetics: analysis of the forces causing motion The dynamics of a particle are covered in chapters 12 15 Rigid body dynamics is covered in chapters 16 19
3 Historical Perspective Dynamics could not be studied until accurate measurements of time were developed Galileo Galilei (1564 1642), was one of the first contributors, by investigating pendulums and falling bodies Isaac Newton (1642 1727), founded the laws of motion and gravitational attraction Recommended Steps to Solve Dynamics Problems 1. Read the problem carefully and try to correlate the actual physical situation with the theory studied 2. Draw the necessary diagrams and tabulate the data 3. Establish a coordinate system and apply the relevant principles 4. Solve the necessary equations algebraically 5. Review the answer to see if it makes sense 6. Review the problem, where there other ways to solve the problem

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4 12.2 Rectilinear Kinematics: Continuous Motion This discussion will concern the motion of a particle along a straight path By definition, a particle has a mass but negligible size and shape In reality, this analysis must be applied sparingly, where the size has little to no effect on the motion For objects with a size, this analysis may be used, if we discuss the motion of the bodies mass center and neglect any rotation of the body Rectilinear Kinematics The kinematics of a particle is characterized by specifying (at a given instant in time) the particles position velocity and acceleration Position coordinate, is defined using a single coordinate axis, ݏ The origin on this path is ܱ The magnitude of ݏ is the distance of the particle from ܱ This is used to determine the location of any particle Note, that position is a vector quantity because there is both magnitude and direction (although the direction under these conditions is arbitrary and usually set as positive)!
5 Displacement This is defined as the change in the particles position As the particle moves from one point to another, we can mathematically represent displacement as Δݏ ൌ ݏ

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Chapter_12_mod - Chapter12:Kinematicsofa Particle...

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