Mechanics

Overview

Mechanics is a basic course for studying the laws of mechanical movement. Through this course, students can acquire knowledge, and more importantly, master the subject system and the methods of solving problems. This course will help students to develop logical thinking and to cultivate the ability of accepting new ideas, laying a solid foundation for subsequent courses. The basic teaching requirement of this course is to clarify the logical structure and knowledge system of Mechanics. Through resources such as the application cases, 55 AR demos, 60 animation demos, 51 video recordings, and the audio recordings of biographies of 25 scientific giants in the field of mechanical movement, students will appreciate the beauty of Mechanics and the truth of human civilization, as well as master the general methods of solving mechanical problems. Furthermore, a brief history of the development of Physics and some concepts in modern Physics are incorporated into the relevant chapters to stimulate students’ thinking and cultivate their ability to accept new ideas.

Syllabus

Introduction

0.1-1 Research contents of Physics
0.1-2 Research methods of Physics
0.1-3 Practical use of Physics
0.2 A logical overview of mechanical movement laws
0.3-0 Development history of mechanical movement laws
0.3-1 Look up at the heaven
0.3-2 Bend down to the earth
0.3-3 Unite the heaven and the earth
0.3-4 Theory instruction
0.3-5 Further development
0.4-1 Status and role of Mechanics in Physics
0.4-2 Body of knowledge for Mechanics
0.5 Advices on Physics learning
0.6 Basic Vector Operations

Chapter 1: Kinematics of point mass

1. Summary of Point Mass Kinematics
1.1.1 Point mass, reference system and coordinate system
1.1.2 Position vector, displacement, velocity, acceleration and their relationship
1.2.1 Representation in rectangular coordinate system
1.2.2 Representation in plane polar coordinate system
1.2.3 Representation in intrinsic coordinate system
1.3 Relative motion
1.3.1 Transformations of velocity and acceleration between translational and static reference systems
1.3.2 Transformations of velocity and acceleration between uniformly rotating and static reference systems
1.4 Brief summary of Chapter 1

Chapter 2：Dynamics of point mass in the inertial system

2. Point Mass Dynamics in the Inertial Reference System
2.1.1 Newton's First Law
2.1.2 Newton's Second Law
2.1.3 Newton's Third Law
2.2.1 Kepler's Three Laws
2.2.2 Establishment of the Law of Gravitation
2.3.1 Common forces in nature
2.3.2 Common forces in Mechanics
2.4.1-2.4.3 Dimensions
2.4.4 Measurement of time, length and mass
2.5 Brief summary of Chapter 2

Chapter 3: Dynamics of point mass in non-inertial system

3. Point Mass Dynamics in the Non-inertial Reference System
3.1 Principle of Relativity
3.2 Point Mass Dynamics in the Non-inertial Reference System
3.2.1 Inertial Force in Non-inertial Reference System in Accelerated Translational Motion
3.2.2 Inertial Force in Non-inertial Reference System Rotating at A Constant Angular Velocity
3.2.3 Summary of inertial frame and inertial frame particle dynamics equations
3.3.1 Nature of Inertia for Translational Inertial Force, Overweight and Weightlessness, and Tides due to Translational Inertial Force
3.3.2 Apparent Gravity due to Inertial Centrifugal Force
3.3.3 Foucault Pendulum Experiment, Eastward Deviation of the Falling Body, Northeast Trade Wind, Typhoon and Atmospheric Circulation due to Coriolis Inertial Force
3.4 Essentials of Inertia Force
3.5 Brief summary of Chapter 3

Chapter 4： Momentum theorem and conservation law of point mass group

4. General Introduction to Momentum Theorem and the Law of Conservation of Momentum
4.1.1 Center of Mass of A Point Mass Group and the Motion Law of the Center of Mass
4.1.2 Characteristics and Finding of the Center of Mass
4.1.3 Center-of-mass Frame
4.2.1 Momentum Theorem of the Point Mass
4.2.2 Momentum Theorem of the Point Mass Group
4.2.3 Momentum Theorem of the Center of Mass
4.2.4 Conservation of Momentum of the Point Mass Group
4.2.5 Total Momentum of Point Mass Group in A Center-of-mass Frame
4.3.1 Kinetic Equation in the Variable Mass System
4.3.2 Concrete Examples of the Kinetic Equation in A Variable Mass System
4.4 Brief Summary of This Chapter 4

Chapter 5: Work-energy principle and conservation law of point mass group

5. A Brief Introducton on Work-energy Principle and Law of Conservation of Mechanical Energy
5.1.1 Kinetic Energy Theorem of Point Mass
5.1.2 Work and Power of the Force
5.1.3 Kinetic Energy Theorem of Point Mass System
5.2.1 Characteristics of the Work of A Pair of Internal Forces
5.2.2 Conservative Internal Force and Non-conservative Internal Force
5.2.3 Potential Energy of Point Mass System
5.3.1 Work-energy Principle of Point Mass System
5.3.2 Law of Conservation of Mechanical Energy of Point Mass System
5.3.3 Relation between Kinetic Energy of Point Mass System in a Stationary System and That in a Center-of-mass Frame
5.3.4 Work-energy Principle of Point Mass System in a Center-of-mass Frame
5.3.5 The Law of Energy Conservation
5.4.1 Features of Collision
5.4.2 Process of One-dimensional Collision and Its Classification
5.4.3 Law of Collision
5.4.4 Two-dimensional Collision
5.5 Brief Summary of Chapter 5

Chapter 6: Angular momentum theorem and conservation law of particle point mass group

6. A Brief Introduction to Angular Momentum Theorem and Conservation Law of Angular Momentum
6.1.1 Angular Momentum Theorem of Point Mass
6.1.2 Torque of Force
6.1.3 Angular Momentum of Point Mass
6.1.4 Angular Momentum Conservation of Point Mass
6.2.1 Angular Momentum Theorem of Point Mass System
6.2.2 Angular Momentum Conservation of Point Mass System
6.2.3 Relationship between Angular Momentum of the Point Mass System in the Stationary System and That in the Center-of-mass Frame
6.2.4 Angular Momentum Theorem of Point Mass System in the Center-of-mass Frame
6.3.1 Three Cosmic Velocities
★6.3.2 Effective Potential Energy and Orbital Property
6.3.3 Transforming Two Objects into One
6.4 Conservation Laws and Symmetry
6.5 Brief Summary of Chapter 6

Chapter 7: Rigid body

7. General of Rigid Body
7.1.1 The Rotational Quantities to Describe the Rotation of Rigid Body around A Fixed Axis
7.1.2 The Vector Analysis of the Rotational Quantities
7.1.3 The Relationship between Rotational Angular Quantities and Linear Quantities
7.2.1 Potential Energy, Kinetic Energy, Angular Momentum and the Work of External Forces for Rigid Body Rotating around A Fixed Axis
7.2.2 Moment of Inertia
7.2.3 The Law of Rotation for Rigid Body Rotating around A Fixed Axis
7.2.4 Angular Momentum Theorem and the Conservation Law for Rigid Body Rotating around A Fixed Axis
7.2.5 Kinetic Energy Theorem of Rigid Body Rotating around A Fixed Axis
7.3.1 The Force System Acting on A Rigid Body and Its Equivalence
7.3.2 The Method of Dealing with the Plane Parallel Motion of A Rigid Body
7.4.1 Expressions of Kinetic Energy and Angular Momentum for Plane Parallel Motion
7.4.2 Equations of Translation and Rotation of Rigid Body
7.4.3-1 Problem of the Force on the Axis
7.4.3-2 Problem of Collision between the Point Mass and the Lever
7.4.3-3 Problem of Pure Rolling
7.4.3-4 Rolling Friction
7.4.3-5 Other forms of plane parallel motion
7.5.1 Instantaneous Rotation Axis of Rigid Body
7.5.2 Kinetic Energy Theorem of Rotation around An Instantaneous Axis
7.5.3 Law of Rotation around An Instantaneous Axis
7.6 Equilibrium of Rigid Body
7.7.1 Motion of Rigid Body without Influence of External Torque
7.7.2 Precession of Rigid Body under the Effect of External Torque
7.8 Brief Summary of This Chapter 7

Chapter 8: Fluid

8. General of Fluid
8.1.1 Pressure at Any Point in Static Fluid
8.1.2 Relationship between Pressures at Different Points in Static Fluid
8.1.3 The Buoyancy Law (Archimedes Principle)
8.1.4 Pascal's Law
8.2.1 Description of Flowing Fluid
8.2.2 Any Pressure in Flowing Fluid
8.2.3 Continuity Equation
8.2.4 Bernoulli Equation
8.2.5 Momentum and Angular Momentum of Fluid
8.3.1 Examples of Daily Life Phenomena, Such as Lift Force of the Wing and Magnus Effect
8.3.2 Orifice Flow Measurement
8.3.3 Measurement of Liquid Velocity in Pipe - Venturi Flowmeter
8.3.4 Measurement of Liquid Velocity in Non-pipe - Pitot Tube
8.3.5 Siphon Phenomenon
8.4.1 Newtonian and Non-Newtonian Fluids
8.5 Brief Summary of This Chapter

Chapter 9: Vibration

9. General of Vibration
9.1.1 The Kinetic Equation of Simple Harmonic Vibration and Its Solution
9.1.2 The Kinematic Features of Simple Harmonic Vibration
9.1.3 The Geometric Representation of Simple Harmonic Vibration
9.1.4-1 Synthesis of the Simple Harmonic Vibration with the Same Direction and Frequency
9.1.4-2 Synthesis of the Simple Harmonic Vibration with the Same Direction and Different Frequency-beat Phenomenon
9.1.4-3 Synthesis of Simple Harmonic Vibrations with the Same Frequency in Mutually Perpendicular Directions
9.1.4-4 Synthesis of Simple Harmonic Vibrations in Integral-multiple Frequency Relationship in Perpendicular Directions-Lissajou Figure
9.2.1 Differential Equation and Solutions of the Damped Vibration
9.3.1 Differential Equation and Solutions of the Forced Vibration
9.3.2 Resonance Phenomenon of the Forced Vibration
9.4 Brief Summary of This Chapter

Chapter 10: Fluctuation

10. General of Fluctuation
10.1.1 Conditions and Features of Mechanical Wave
10.1.2 Geometric Description of Mechanical Wave
10.1.3 Classification of Wave
10.2.1 Wave Equation of Tensioned String
10.2.2 Elastic Wave Equation in Solid Body
10.3.1 Solution to the Mechanical Wave Equation
10.3.2 Classification of the Propagation Forms of Wave
10.3.3 Phase Velocity and Group Velocity of Wave
10.4.1 Physical Quantities Describing the Features of the Simple Harmonic Wave
10.4.2 Phase Transfer Method for the Expression of Simple Harmonic Wave
10.4.3 Some Common Expressions of the Plane Simple Harmonic Wave
10.5.1 Energy of the Traveling Wave
10.5.2 Wave Diffraction and Huygens Principle
10.5.3 Superposition Principle of the Wave
10.5.4 Reflection and Transmission of Waves at An Interface
10.5.5 Standing Wave
10.5.6 Normal Frequency
10.6 Doppler Effect
★10.7 Introduction to Sound Wave and Super Wave Velocity Motion
10.8 Brief Summary of This Chapter

Chapter 11: Special relativity

11. Introduction To Special Relativity
11.1.1 Classical Spatial-temporal Perspective Contained in Galileo Transformation
11.1.2 Michelson-Morley Experiment
11.2 Two Basic Hypotheses of Special Relativity
11.3.1 Lorentz Transformation
11.3.2 Lorentz Transformation and Transformation of Velocity and Acceleration
11.3.3 Comparison of Galileo Transformation and Lorentz Transformation
11.4.1 Relativity of Simultaneity
11.4.2 Time Dilation
11.4.3 Length Contraction
11.4.4 Clock Synchronization
11.4.5 Doppler Effect
11.5 Fundamental Equation in Dynamics
11.6 Brief Summary of This Chapter