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Solving Physics Problems

Exploring New Thinking Paradigms

by Yipeng Gu

“Solving problems in physics is time-consuming, challenging, yet highly rewarding. It is an efficient way to master physics. Dr. Gu is an expert and has been coaching in this field for almost 20 years. This remarkable book is the crystallization of his talent and longterm effort. It provides a featured thinking paradigm and systematic analysis on plenty of models, making it distinguished from other popular books. By reading this book, you may develop problem-solving skills and also gain confidence on physics theories.” Prof. Fawei Zheng, Beijing Institute of Technology, China

• Format: Hardcover
• ISBN : 9789814877411
• Subject : General Materials Science
• Published : August 2022
• Pages : 806

USD $149.95

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This book provides a complete, self-consistent, and open system for studying physics problems, which not only provides high-quality teaching materials for the field of physics education (especially for physics Olympiad training) but also points out a new direction for physics education. In this book, a form of methodology, which can comprehensively present cogitation discipline, is built up for analyzing and solving complex physics problems. The text analyzes plenty of physics problems (classical mechanics) from both theoretical and philosophical points of view to reveal the way of exerting this form. As a set of methodology reflecting the cogitation discipline, the thinking paradigm proposed in this book (called the MLQ-(ST)C paradigm) is a theoretical tool to cultivate people to acquire this ability. The paradigm successfully deconstructs the elements and the structure in physical thinking and then eliminates the obstacles of people’s underlying thinking, so that all the thinking built on it can be clear and ordered. The physics problems included in this book are much more difficult than similar books within the same theoretical domains involved, leading to better teaching and learning value.

Solving Physics Problems : Chapter has no title

Pages: 15-112

Pages: 113-316

Pages: 317-450

Pages: 451-602

Two-Body Model

Pages: 603-716

Pages: 717-774

Yipeng Gu obtained his PhD in condensed matter physics in 2014 from Jilin University, China. He teaches physics at the School of Natural Science, Changchun University of Science and Technology, China. Dr. Gu’s research interests span the philosophy of physics, theory of physics education, and the innovation and development of physics models. He is an experienced coach for Physics Olympiad and has taught basic courses of college physics and topic courses of physics competition for students who participated in the Chinese Physics Olympiad in Jilin Province, China. His students have won prizes in various levels of physics competitions, including six gold medals in the final contest of Chinese Physics Olympiad.

“Solving problems in physics is time-consuming, challenging, yet highly rewarding. It is an efficient way to master physics. Dr. Gu is an expert and has been coaching in this field for almost 20 years. This remarkable book is the crystallization of his talent and longterm effort. It provides a featured thinking paradigm and systematic analysis on plenty of models, making it distinguished from other popular books. By reading this book, you may develop problem-solving skills and also gain confidence on physics theories.” ~Prof. Fawei Zheng, Beijing Institute of Technology, China

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• Classical Mechanics

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Online textbook.

These notes were updated in 2022 to reflect corrections that readers have noticed.

Chapter 1: Introduction to Classical Mechanics (PDF)

Chapter 2: Units, Dimensional Analysis, Problem Solving, and Estimation (PDF - 4.5 MB)

Chapter 3: Vectors (PDF - 4.4 MB)

Chapter 4: One Dimensional Kinematics (PDF - 3.2 MB)

Chapter 5: Two Dimensional Kinematics (PDF - 2.3 MB)

Chapter 6: Circular Motion (PDF - 2.6 MB)

Chapter 7: Newton’s Laws of Motion (PDF)

Chapter 8: Applications of Newton’s Second Law (PDF - 6 MB)

Chapter 9: Circular Motion Dynamics (PDF - 2.4 MB)

Chapter 10: Momentum, System of Particles, and Conservation of Momentum (PDF - 3 MB)

Chapter 11: Reference Frames (PDF - 1.4 MB)

Chapter 12: Momentum and the Flow of Mass (PDF - 3.3 MB)

Chapter 13: Energy, Kinetic Energy, and Work (PDF - 5.1 MB)

Chapter 14: Potential Energy and Conservation of Energy (PDF - 6.1 MB)

Chapter 15: Collision Theory (PDF - 3.3 MB)

Chapter 16: Two Dimensional Rotational Kinematics (PDF - 2.4 MB)

Chapter 17: Two Dimensional Rotational Dynamics (PDF - 4 MB)

Chapter 18: Static Equilibrium (PDF - 2.2 MB)

Chapter 19: Angular Momentum (PDF - 4.2 MB)

Chapter 20: Rigid Body Kinematics About a Fixed Axis (PDF - 3.1 MB)

Chapter 21: Rigid Body Dynamics About a Fixed Axis (PDF - 4.4 MB)

Chapter 22: Three Dimensional Rotations and Gyroscopes (PDF - 3.5 MB)

Chapter 23: Simple Harmonic Motion (PDF - 5.9 MB)

Chapter 24: Physical Pendulum (PDF - 2.3 MB)

Chapter 25: Celestial Mechanics (PDF - 4.5 MB)

Chapter 26: Elastic Properties of Materials (PDF - 2.6 MB)

Chapter 27: Static Fluids (PDF - 1.8 MB)

Chapter 28: Fluid Dynamics (PDF - 2.5 MB)

Chapter 29: Kinetic Theory of Gases (PDF - 1.8 MB)

Chapter 30: Navier Stokes Equation (PDF - 2.2 MB)

Chapter 31: Non-Inertial Linear and Rotating Reference Frames (PDF - 6 MB)

Physical Constants (PDF)

Astronomical Data (PDF)

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Physics is a branch of science that studies the properties of matter, energy, and many more. Physics is considered to be the most fundamental of all the sciences, and is also the oldest.

• 2 History of Physics
• 3.1 Isaac Newton
• 3.2 Albert Einstein
• 4 Classical Mechanics
• 5 Statistical Mechanics
• 6 Acoustics
• 8 Thermodynamics
• 9 Electromagnetism
• 10 See also

Physics before the 19th century is called Classical Physics . Physics after the 19th century is know as Modern Physics .

Classical Physics can be split even further into its own branches:

• Classical Mechanics
• Statistical Mechanics
• Thermodynamics
• Electromagnetism

Modern Physics is also a group of different subjects in physics:

• Quantum Mechanics
• Nuclear Physics
• Condensed Matter Physics
• Particle Physics
• Astrophysics

History of Physics

The history of physics is long and exciting. Physics started with the first scientist, Thales of Miletus, who was the first to try to systematically explain the world using theories and hypotheses instead of using gods and magic. Archimedes also made a big breakthrough in physics when he devised the concept of buoyancy . This discovery was in the third century BC and not much innovation was made thereafter for many centuries.

However, Galileo Galilei, an Italian scientist, first advocated for the systematic study of physics. He was the one who tried to preach his scientific thoughts about how the Earth orbited the Sun, opposing the ideas of the Catholic establishment, and became the first patron of physics.

This was then further developed by Sir Isaac Newton , an English scientist, who devised the modern study of physics by discovering many laws. Since then, physics has never looked back!

Notable Figures

Isaac newton.

Isaac Newton was born on January 4, 1643, in Lincolnshire, England. Newton was born very shortly after the death of his father. He did very well at his local school and later attended Trinity College.

What is now considered Newton's most famous achievement is the formal statement of three basic, almost trivial laws of motion:

• If the net force on any amount of matter is Zero , then the object's velocity will not change if viewing from a constant reference point.

A Handbook of Mathematical Methods and Problem-Solving Tools for Introductory Physics

Authors Joshua F Whitney and Heather M Whitney Published October 2016

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This is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.

Copyright © 2016 Morgan & Claypool Publishers Online ISBN: 978-1-6817-4281-6 • Print ISBN: 978-1-6817-4280-9

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Front matter

Introduction.

Joshua F Whitney and Heather M Whitney

Newton's laws

Energy and momentum, circular and rotational motion, basic optics, the right-hand rule, electric fields and electric potential, modern physics, general problem-solving tips, d o i.

https://doi.org/10.1088/978-1-6817-4281-6

Recommended reading for anyone studying introductory course in physics

Published October 2016

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About the authors

Joshua F Whitney and Heather M Whitney are both teachers in the Department of Physics at Wheaton College. Joshua completed his PhD in physics at the University of Tennessee, working in theoretical particle physics. He has spent considerable time teaching introductory and upper-level physics classes and labs. Heather completed her PhD in physics at Vanderbilt University, doing research in the Vanderbilt University Institute for Imaging Science. In addition to teaching, she works with undergraduate students on research projects in medical physics.

• General Physics
• Theoretical Physics

Problem Solving in Theoretical Physics

ISBN: 978-3-527-41396-6

August 2020

Digital Evaluation Copy

Yury M. Belousov , Serguei N. Burmistrov , Alexei I. Ternov

Yury M. Belousov is Researcher and Lecturer at the Moscow Institute of Physics and Technology, Dolgoprudny, Russia.

Serguei N. Burmistrov is Researcher and Lecturer at the Russian Research Center "Kurchatov Institute", Moscow, Russia.

Alexei I. Ternov is Researcher and Lecturer at the Moscow Institute of Physics and Technology, Dolgoprudny, Russia.

1st Edition

Solving Physics Problems Exploring New Thinking Paradigms

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Description

This book provides a complete, consistent, and open system for studying physics problems, which not only provides high-quality teaching materials for the field of physics education (especially for Physics Olympiad training) but also points out a new direction for physics education. In this book, a form of methodology, which can comprehensively present cogitation discipline, is built up for analyzing and solving complex physics problems. The text analyzes plenty of physics problems (classical mechanics) from both theoretical and philosophical points of view to reveal the way of exerting this form. As a set of methodology reflecting the cogitation discipline, the thinking paradigm proposed in this book (called the MLQ-(ST)C paradigm) is a theoretical tool to develop people's acquisition of this ability. The paradigm successfully deconstructs the elements and the structure in physical thinking and then eliminates the obstacles of people’s underlying thinking, so that all the thinking built on it can be clear and ordered. The physics problems included in this book are significantly more difficult than similar books within the same theoretical domains involved, leading to better teaching and learning value.

Table of Contents

Yipeng Gu obtained his PhD in condensed matter physics in 2014 from Jilin University, China. He teaches physics at the School of Natural Science, Changchun University of Science and Technology, China. Dr. Gu’s research interests span the philosophy of physics, theory of physics education, and the innovation and development of physics models. He is an experienced coach for Physics Olympiad and has taught basic courses of college physics and topic courses of physics competition for students who participated in the Chinese Physics Olympiad in Jilin Province, China. His students have won prizes in various levels of physics competitions, including six gold medals in the final contest of the Chinese Physics Olympiad.

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4.6 Problem-Solving Strategies

Learning objectives.

By the end of this section, you will be able to:

• Understand and apply a problem-solving procedure to solve problems using Newton's laws of motion.

Success in problem solving is obviously necessary to understand and apply physical principles, not to mention the more immediate need of passing exams. The basics of problem solving, presented earlier in this text, are followed here, but specific strategies useful in applying Newton’s laws of motion are emphasized. These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop.

Problem-Solving Strategy for Newton’s Laws of Motion

Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newton’s laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation . Such a sketch is shown in Figure 4.20 (a). Then, as in Figure 4.20 (b), use arrows to represent all forces, label them carefully, and make their lengths and directions correspond to the forces they represent (whenever sufficient information exists).

Step 2. Identify what needs to be determined and what is known or can be inferred from the problem as stated. That is, make a list of knowns and unknowns. Then carefully determine the system of interest . This decision is a crucial step, since Newton’s second law involves only external forces. Once the system of interest has been identified, it becomes possible to determine which forces are external and which are internal, a necessary step to employ Newton’s second law. (See Figure 4.20 (c).) Newton’s third law may be used to identify whether forces are exerted between components of a system (internal) or between the system and something outside (external). As illustrated earlier in this chapter, the system of interest depends on what question we need to answer. This choice becomes easier with practice, eventually developing into an almost unconscious process. Skill in clearly defining systems will be beneficial in later chapters as well. A diagram showing the system of interest and all of the external forces is called a free-body diagram . Only forces are shown on free-body diagrams, not acceleration or velocity. We have drawn several of these in worked examples. Figure 4.20 (c) shows a free-body diagram for the system of interest. Note that no internal forces are shown in a free-body diagram.

Step 3. Once a free-body diagram is drawn, Newton’s second law can be applied to solve the problem . This is done in Figure 4.20 (d) for a particular situation. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples. If the problem is one-dimensional—that is, if all forces are parallel—then they add like scalars. If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems. This is done by projecting the force vectors onto a set of axes chosen for convenience. As seen in previous examples, the choice of axes can simplify the problem. For example, when an incline is involved, a set of axes with one axis parallel to the incline and one perpendicular to it is most convenient. It is almost always convenient to make one axis parallel to the direction of motion, if this is known.

Applying Newton’s Second Law

Before you write net force equations, it is critical to determine whether the system is accelerating in a particular direction. If the acceleration is zero in a particular direction, then the net force is zero in that direction. Similarly, if the acceleration is nonzero in a particular direction, then the net force is described by the equation: F net = ma F net = ma .

For example, if the system is accelerating in the horizontal direction, but it is not accelerating in the vertical direction, then you will have the following conclusions:

You will need this information in order to determine unknown forces acting in a system.

Step 4. As always, check the solution to see whether it is reasonable . In some cases, this is obvious. For example, it is reasonable to find that friction causes an object to slide down an incline more slowly than when no friction exists. In practice, intuition develops gradually through problem solving, and with experience it becomes progressively easier to judge whether an answer is reasonable. Another way to check your solution is to check the units. If you are solving for force and end up with units of m/s, then you have made a mistake.

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Problem-Solving Exercises in Physics: The High School Physics Program (Prentice Hall Conceptual Physics Workbook)

• ISBN-10 013054275X
• ISBN-13 978-0130542755
• Publisher Pearson Prentice Hall
• Publication date January 1, 2002
• Language English
• Dimensions 8.25 x 0.5 x 10.75 inches
• Print length 256 pages
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• Grade level ‏ : ‎ 10 - 12
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• Dimensions ‏ : ‎ 8.25 x 0.5 x 10.75 inches
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The Impact of Topic-Specific vs. Generic Self-reflection on Students’ Metacognitive Abilities, Conceptual Understanding, and Problem-Solving Strategies

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