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Format: 1 online resource (179 pages)

Edition: 1st ed.

ISBN: 9783030151959

Series Statement: Advances in Science, Technology and Innovation Series

Note: 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< -- 2ωn) -- 10.4.2 Critically Damped Motion (γ=2ωn) -- 10.4.3 Over Damped Motion (Heavy Damping) (γ> -- 2ωn) -- 10.4.4 Energy Decay -- 10.5 Forced Vibrations -- References.

Additional Edition: Print version: Alrasheed, Salma Principles of Mechanics Cham : Springer International Publishing AG,c2019 ISBN 9783030151942

Language: English

Subjects: Physics

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UID:

Format: 1 online resource (XI, 173 p. 288 illus., 167 illus. in color.)

Edition: 1st ed. 2019.

ISBN: 3-030-15195-6

Series Statement: Advances in Science, Technology & Innovation, IEREK Interdisciplinary Series for Sustainable Development,

Content: This open access textbook takes the reader step-by-step through the concepts of mechanics in a clear and detailed manner. Mechanics is considered to be the core of physics, where a deep understanding of the concepts is essential in understanding all branches of physics. Many proofs and examples are included to help the reader grasp the fundamentals fully, paving the way to deal with more advanced topics. After solving all of the examples, the reader will have gained a solid foundation in mechanics and the skills to apply the concepts in a variety of situations. The book is useful for undergraduate students majoring in physics and other science and engineering disciplines. It can also be used as a reference for more advanced levels.

Note: Units and Vectors -- Kinematics -- Newton’s Laws -- Work and Energy -- Impulse, Momentum and Collisions -- System of Particles -- Rotation of Rigid Bodies -- Rolling and Static Equilibrium -- Central Force Motion -- Oscillatory Motion. , English

Additional Edition: ISBN 3-030-15194-8

Language: English

DOI: 10.1007/978-3-030-15195-9

UID:

Format: XI, 173 p. 288 illus., 167 illus. in color. , online resource.

Edition: 1st ed. 2019.

ISBN: 9783030151959

Series Statement: Advances in Science, Technology & Innovation, IEREK Interdisciplinary Series for Sustainable Development,

Content: This open access textbook takes the reader step-by-step through the concepts of mechanics in a clear and detailed manner. Mechanics is considered to be the core of physics, where a deep understanding of the concepts is essential in understanding all branches of physics. Many proofs and examples are included to help the reader grasp the fundamentals fully, paving the way to deal with more advanced topics. After solving all of the examples, the reader will have gained a solid foundation in mechanics and the skills to apply the concepts in a variety of situations. The book is useful for undergraduate students majoring in physics and other science and engineering disciplines. It can also be used as a reference for more advanced levels.

Note: Units and Vectors -- Kinematics -- Newton’s Laws -- Work and Energy -- Impulse, Momentum and Collisions -- System of Particles -- Rotation of Rigid Bodies -- Rolling and Static Equilibrium -- Central Force Motion -- Oscillatory Motion.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783030151942

Additional Edition: Printed edition: ISBN 9783030151966

Additional Edition: Printed edition: ISBN 9783030151973

Language: English

DOI: 10.1007/978-3-030-15195-9

URL: https://doi.org/10.1007/978-3-030-15195-9