Table of Contents Contents 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: Rectangular Components 12.6 Motion of a Projectile 12.7 Curvilinear Motion: Normal and Tangential Components 12.8 Curvilinear Motion: Cylindrical Components 12.9 Absolute Dependent Motion Analysis of Two Particles 12.10 Relative-Motion of Two Particles Using Translating Axes 13 Kinetics of a Particle: Force and Acceleration 13.1 Newton’s Second Law of Motion 13.2 The Equation of Motion 13.3 Equation of Motion for a System of Particles 13.4 Equations of Motion: Rectangular Coordinates 13.5 Equations of Motion: Normal and Tangential Coordinates 13.6 Equations of Motion: Cylindrical Coordinates *13.7 Central-Force Motion and Space Mechanics 14 Kinetics of a Particle: Work and Energy 14.1 The Work of a Force 14.2 Principle of Work and Energy 14.3 Principle of Work and Energy for a System of Particles 14.4 Power and Efficiency 14.5 Conservative Forces and Potential Energy 14.6 Conservation of Energy 15 Kinetics of a Particle: Impulse and Momentum 15.1 Principle of Linear Impulse and Momentum 15.2 Principle of Linear Impulse and Momentum for a System of Particles 15.3 Conservation of Linear Momentum for a System of Particles 15.4 Impact 15.5 Angular Momentum 15.6 Relation Between Moment of a Force and Angular Momentum 15.7 Principle of Angular Impulse and Momentum 15.8 Steady Flow of a Fluid Stream *15.9 Propulsion with Variable Mass 16 Planar Kinematics of a Rigid Body 16.1 Planar Rigid-Body Motion 16.2 Translation 16.3 Rotation about a Fixed Axis 16.4 Absolute Motion Analysis 16.5 Relative-Motion Analysis: Velocity 16.6 Instantaneous Center of Zero Velocity 16.7 Relative-Motion Analysis: Acceleration 16.8 Relative-Motion Analysis using Rotating Axes 17 Planar Kinetics of a Rigid Body: Force and Acceleration 17.1 Mass Moment of Inertia 17.2 Planar Kinetic Equations of Motion 17.3 Equations of Motion: Translation 17.4 Equations of Motion: Rotation about a Fixed Axis 17.5 Equations of Motion: General Plane Motion 18 Planar Kinetics of a Rigid Body: Work and Energy 18.1 Kinetic Energy 18.2 The Work of a Force 18.3 The Work of a Couple Moment 18.4 Principle of Work and Energy 18.5 Conservation of Energy 19 Planar Kinetics of a Rigid Body: Impulse and Momentum 19.1 Linear and Angular Momentum 19.2 Principle of Impulse and Momentum 19.3 Conservation of Momentum *19.4 Eccentric Impact 20 Three-Dimensional Kinematics of a Rigid Body 20.1 Rotation About a Fixed Point *20.2 The Time Derivative of a Vector Measured from Either a Fixed or Translating-Rotating System 20.3 General Motion *20.4 Relative-Motion Analysis Using Translating and Rotating Axes 21 Three-Dimensional Kinetics of a Rigid Body *21.1 Moments and Products of Inertia 21.2 Angular Momentum 21.3 Kinetic Energy *21.4 Equations of Motion *21.5 Gyroscopic Motion 21.6 Torque-Free Motion 22 Vibrations *22.1 Undamped Free Vibration *22.2 Energy Methods *22.3 Undamped Forced Vibration *22.4 Viscous Damped Free Vibration *22.5 Viscous Damped Forced Vibration *22.6 Electrical Circuit Analogs A Mathematical Expressions B Vector Analysis C The Chain Rule Fundamental Problems Partial Solutions and Answers