Principles of Mechanics : : Fundamental University Physics.

• Superior document: Advances in Science, Technology and Innovation Series
• Author: Alrasheed, Salma.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2019.; ©2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Series: Advances in Science, Technology and Innovation Series
• Physical Description: 1 online resource (179 pages)

Table of Contents

Intro -- Preface -- Contents -- 1 Units and Vectors -- 1.1 Introduction -- 1.2 The SI Units -- 1.3 Conversion Factors -- 1.4 Dimension Analysis -- 1.5 Vectors -- 1.6 Vector Algebra -- 1.6.1 Equality of Two Vectors -- 1.6.2 Addition -- 1.6.3 Negative of a Vector -- 1.6.4 The Zero Vector -- 1.6.5 Subtraction of Vectors -- 1.6.6 Multiplication of a Vector by a Scalar -- 1.6.7 Some Properties -- 1.6.8 The Unit Vector -- 1.6.9 The Scalar (Dot) Product -- 1.6.10 The Vector (Cross) Product -- 1.7 Coordinate Systems -- 1.8 Vectors in Terms of Components -- 1.8.1 Rectangular Unit Vectors -- 1.8.2 Component Method -- 1.9 Derivatives of Vectors -- 1.9.1 Some Rules -- 1.9.2 Gradient, Divergence, and Curl -- 1.10 Integrals of Vectors -- 1.10.1 Line Integrals -- 1.10.2 Independence of Path -- 2 Kinematics -- 2.1 Introduction -- 2.2 Displacement, Velocity, and Acceleration -- 2.2.1 Displacement -- 2.2.2 Average Speed -- 2.2.3 Velocity -- 2.2.4 Speed -- 2.2.5 Acceleration -- 2.3 Motion in Three Dimensions -- 2.3.1 Normal and Tangential Components of Acceleration -- 2.4 Some Applications -- 2.4.1 One-Dimensional Motion with Constant Acceleration -- 2.4.2 Free-Falling Objects -- 2.4.3 Motion in Two Dimensions with Constant Acceleration -- 2.4.4 Projectile Motion -- 2.4.5 Uniform Circular Motion -- 2.4.6 Nonuniform Circular Motion -- 2.5 Relative Velocity -- 2.6 Motion in a Plane Using Polar Coordinates -- 3 Newton's Laws -- 3.1 Introduction -- 3.1.1 The Concept of Force -- 3.1.2 The Fundamental Forces in Nature -- 3.2 Newton's Laws -- 3.2.1 Newton's First Law -- 3.2.2 The Principle of Invariance -- 3.2.3 Mass -- 3.2.4 Newton's Second Law -- 3.2.5 Newton's Third Law -- 3.3 Some Particular Forces -- 3.3.1 Weight -- 3.3.2 The Normal Force -- 3.3.3 Tension -- 3.3.4 Friction -- 3.3.5 The Drag Force -- 3.4 Applying Newton's Laws -- 3.4.1 Uniform Circular Motion.

3.4.2 Nonuniform Circular Motion -- 4 Work and Energy -- 4.1 Introduction -- 4.2 Work -- 4.2.1 Work Done by a Constant Force -- 4.2.2 Work Done by Several Forces -- 4.2.3 Work Done by a Varying Force -- 4.3 Kinetic Energy (KE) and the Work-Energy Theorem -- 4.3.1 Work Done by a Spring Force -- 4.3.2 Work Done by the Gravitational Force (Weight) -- 4.3.3 Power -- 4.4 Conservative and Nonconservative Forces -- 4.4.1 Potential Energy -- 4.5 Conservation of Mechanical Energy -- 4.5.1 Changes of the Mechanical Energy of a System due to External Nonconservative Forces -- 4.5.2 Friction -- 4.5.3 Changes in Mechanical Energy due to Internal Nonconservative Forces -- 4.5.4 Changes in Mechanical Energy due to All Forces -- 4.5.5 Power -- 4.5.6 Energy Diagrams -- 4.5.7 Turning Points -- 4.5.8 Equilibrium Points -- 4.5.9 Positions of Stable Equilibrium -- 4.5.10 Positions of Unstable Equilibrium -- 4.5.11 Positions of Neutral Equilibrium -- 5 Impulse, Momentum, and Collisions -- 5.1 Linear Momentum and Collisions -- 5.2 Conservation of Linear Momentum -- 5.3 Impulse and Momentum -- 5.4 Collisions -- 5.4.1 Elastic Collisions -- 5.4.2 Inelastic Collisions -- 5.4.3 Elastic Collision in One Dimension -- 5.4.4 Inelastic Collision in One Dimension -- 5.4.5 Coefficient of Restitution -- 5.4.6 Collision in Two Dimension -- 5.5 Torque -- 5.6 Angular Momentum -- 5.6.1 Newton's Second Law in Angular Form -- 5.6.2 Conservation of Angular Momentum -- 6 System of Particles -- 6.1 System of Particles -- 6.2 Discrete and Continuous System of Particles -- 6.2.1 Discrete System of Particles -- 6.2.2 Continuous System of Particles -- 6.3 The Center of Mass of a System of Particles -- 6.3.1 Two Particle System -- 6.3.2 Discrete System of Particles -- 6.3.3 Continuous System of Particles (Extended Object) -- 6.3.4 Elastic and Rigid Bodies -- 6.3.5 Velocity of the Center of Mass.

6.3.6 Momentum of a System of Particles -- 6.3.7 Motion of a System of Particles -- 6.3.8 Conservation of Momentum -- 6.3.9 Angular Momentum of a System of Particles -- 6.3.10 The Total Torque on a System -- 6.3.11 The Angular Momentum and the Total External Torque -- 6.3.12 Conservation of Angular Momentum -- 6.3.13 Kinetic Energy of a System of Particles -- 6.3.14 Work -- 6.3.15 Work-Energy Theorem -- 6.3.16 Potential Energy and Conservation of Energy of a System of Particles -- 6.3.17 Impulse -- 6.4 Motion Relative to the Center of Mass -- 6.4.1 The Total Linear Momentum of a System of Particles Relative to the Center of Mass -- 6.4.2 The Total Angular Momentum About the Center of Mass -- 6.4.3 The Total Kinetic Energy of a System of Particles About the Center of Mass -- 6.4.4 Total Torque on a System of Particles About the Center of Mass of the System -- 6.4.5 Collisions and the Center of Mass Frame of Reference -- 7 Rotation of Rigid Bodies -- 7.1 Rotational Motion -- 7.2 The Plane Motion of a Rigid Body -- 7.2.1 The Rotational Variables -- 7.3 Rotational Motion with Constant Acceleration -- 7.4 Vector Relationship Between Angular and Linear Variables -- 7.5 Rotational Energy -- 7.6 The Parallel-Axis Theorem -- 7.7 Angular Momentum of a Rigid Body Rotating about a Fixed Axis -- 7.8 Conservation of Angular Momentum of a Rigid Body Rotating About a Fixed Axis -- 7.9 Work and Rotational Energy -- 7.10 Power -- 8 Rolling and Static Equilibrium -- 8.1 Rolling Motion -- 8.2 Rolling Without Slipping -- 8.3 Static Equilibrium -- 8.4 The Center of Gravity -- 9 Central Force Motion -- 9.1 Motion in a Central Force Field -- 9.1.1 Properties of a Central Force -- 9.1.2 Equations of Motion in a Central Force Field -- 9.1.3 Potential Energy of a Central Force -- 9.1.4 The Total Energy -- 9.2 The Law of Gravity.

9.2.1 The Gravitational Force Between a Particle and a Uniform Spherical Shell -- 9.2.2 The Gravitational Force between a Particle and a Uniform Solid Sphere -- 9.2.3 Weight and Gravitational Force -- 9.2.4 The Gravitational Field -- 9.3 Conic Sections -- 9.3.1 The Polar Equation of a Conic Section -- 9.3.2 Motion in a Gravitational Force Field -- 9.3.3 The Gravitational Potential Energy -- 9.3.4 Energy in a Gravitational Force Field -- 9.4 Kepler's Laws -- 9.4.1 Kepler's First Law -- 9.4.2 Kepler's Second Law -- 9.4.3 Kepler's Third Law -- 9.5 Circular Orbits -- 9.6 Elliptical Orbits -- 9.7 The Escape Speed -- 10 Oscillatory Motion -- 10.1 Oscillatory Motion -- 10.2 Free Vibrations -- 10.3 Free Undamped Vibrations -- 10.3.1 Mass Attached to a Spring -- 10.3.2 Simple Harmonic Motion and Uniform Circular Motion -- 10.3.3 Energy of a Simple Harmonic Oscillator -- 10.3.4 The Simple Pendulum -- 10.3.5 The Physical Pendulum -- 10.3.6 The Torsional Pendulum -- 10.4 Damped Free Vibrations -- 10.4.1 Light Damping (Under-Damped) (γ&lt -- 2ωn) -- 10.4.2 Critically Damped Motion (γ=2ωn) -- 10.4.3 Over Damped Motion (Heavy Damping) (γ&gt -- 2ωn) -- 10.4.4 Energy Decay -- 10.5 Forced Vibrations -- References.