1.1 Physics: An Introduction

Learning objectives.

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

  • Explain the difference between a principle and a law.
  • Explain the difference between a model and a theory.

The physical universe is enormously complex in its detail. Every day, each of us observes a great variety of objects and phenomena. Over the centuries, the curiosity of the human race has led us collectively to explore and catalog a tremendous wealth of information. From the flight of birds to the colors of flowers, from lightning to gravity, from quarks to clusters of galaxies, from the flow of time to the mystery of the creation of the universe, we have asked questions and assembled huge arrays of facts. In the face of all these details, we have discovered that a surprisingly small and unified set of physical laws can explain what we observe. As humans, we make generalizations and seek order. We have found that nature is remarkably cooperative—it exhibits the underlying order and simplicity we so value.

It is the underlying order of nature that makes science in general, and physics in particular, so enjoyable to study. For example, what do a bag of chips and a car battery have in common? Both contain energy that can be converted to other forms. The law of conservation of energy (which says that energy can change form but is never lost) ties together such topics as food calories, batteries, heat, light, and watch springs. Understanding this law makes it easier to learn about the various forms energy takes and how they relate to one another. Apparently unrelated topics are connected through broadly applicable physical laws, permitting an understanding beyond just the memorization of lists of facts.

The unifying aspect of physical laws and the basic simplicity of nature form the underlying themes of this text. In learning to apply these laws, you will, of course, study the most important topics in physics. More importantly, you will gain analytical abilities that will enable you to apply these laws far beyond the scope of what can be included in a single book. These analytical skills will help you to excel academically, and they will also help you to think critically in any professional career you choose to pursue. This module discusses the realm of physics (to define what physics is), some applications of physics (to illustrate its relevance to other disciplines), and more precisely what constitutes a physical law (to illuminate the importance of experimentation to theory).

Science and the Realm of Physics

Science consists of the theories and laws that are the general truths of nature as well as the body of knowledge they encompass. Scientists are continually trying to expand this body of knowledge and to perfect the expression of the laws that describe it. Physics is concerned with describing the interactions of energy, matter, space, and time, and it is especially interested in what fundamental mechanisms underlie every phenomenon. The concern for describing the basic phenomena in nature essentially defines the realm of physics .

Physics aims to describe the function of everything around us, from the movement of tiny charged particles to the motion of people, cars, and spaceships. In fact, almost everything around you can be described quite accurately by the laws of physics. Consider a smart phone ( Figure 1.3 ). Physics describes how electricity interacts with the various circuits inside the device. This knowledge helps engineers select the appropriate materials and circuit layout when building the smart phone. Next, consider a GPS system. Physics describes the relationship between the speed of an object, the distance over which it travels, and the time it takes to travel that distance. GPS relies on precise calculations that account for variations in the Earth's landscapes, the exact distance between orbiting satellites, and even the effect of a complex occurrence of time dilation. Most of these calculations are founded on algorithms developed by Gladys West, a mathematician and computer scientist who programmed the first computers capable of highly accurate remote sensing and positioning. When you use a GPS device, it utilizes these algorithms to recognize where you are and how your position relates to other objects on Earth.

Applications of Physics

You need not be a scientist to use physics. On the contrary, knowledge of physics is useful in everyday situations as well as in nonscientific professions. It can help you understand how microwave ovens work, why metals should not be put into them, and why they might affect pacemakers. (See Figure 1.4 and Figure 1.5 .) Physics allows you to understand the hazards of radiation and rationally evaluate these hazards more easily. Physics also explains the reason why a black car radiator helps remove heat in a car engine, and it explains why a white roof helps keep the inside of a house cool. Similarly, the operation of a car’s ignition system as well as the transmission of electrical signals through our body’s nervous system are much easier to understand when you think about them in terms of basic physics.

Physics is the foundation of many important disciplines and contributes directly to others. Chemistry, for example—since it deals with the interactions of atoms and molecules—is rooted in atomic and molecular physics. Most branches of engineering are applied physics. In architecture, physics is at the heart of structural stability, and is involved in the acoustics, heating, lighting, and cooling of buildings. Parts of geology rely heavily on physics, such as radioactive dating of rocks, earthquake analysis, and heat transfer in the Earth. Some disciplines, such as biophysics and geophysics, are hybrids of physics and other disciplines.

Physics has many applications in the biological sciences. On the microscopic level, it helps describe the properties of cell walls and cell membranes ( Figure 1.6 and Figure 1.7 ). On the macroscopic level, it can explain the heat, work, and power associated with the human body. Physics is involved in medical diagnostics, such as x-rays, magnetic resonance imaging (MRI), and ultrasonic blood flow measurements. Medical therapy sometimes directly involves physics; for example, cancer radiotherapy uses ionizing radiation. Physics can also explain sensory phenomena, such as how musical instruments make sound, how the eye detects color, and how lasers can transmit information.

It is not necessary to formally study all applications of physics. What is most useful is knowledge of the basic laws of physics and a skill in the analytical methods for applying them. The study of physics also can improve your problem-solving skills. Furthermore, physics has retained the most basic aspects of science, so it is used by all of the sciences, and the study of physics makes other sciences easier to understand.

Models, Theories, and Laws; The Role of Experimentation

The laws of nature are concise descriptions of the universe around us; they are human statements of the underlying laws or rules that all natural processes follow. Such laws are intrinsic to the universe; humans did not create them and so cannot change them. We can only discover and understand them. Their discovery is a very human endeavor, with all the elements of mystery, imagination, struggle, triumph, and disappointment inherent in any creative effort. (See Figure 1.8 and Figure 1.9 .) The cornerstone of discovering natural laws is observation; science must describe the universe as it is, not as we may imagine it to be.

We all are curious to some extent. We look around, make generalizations, and try to understand what we see—for example, we look up and wonder whether one type of cloud signals an oncoming storm. As we become serious about exploring nature, we become more organized and formal in collecting and analyzing data. We attempt greater precision, perform controlled experiments (if we can), and write down ideas about how the data may be organized and unified. We then formulate models, theories, and laws based on the data we have collected and analyzed to generalize and communicate the results of these experiments.

A model is a representation of something that is often too difficult (or impossible) to display directly. While a model is justified with experimental proof, it is only accurate under limited situations. An example is the planetary model of the atom in which electrons are pictured as orbiting the nucleus, analogous to the way planets orbit the Sun. (See Figure 1.10 .) We cannot observe electron orbits directly, but the mental image helps explain the observations we can make, such as the emission of light from hot gases (atomic spectra). Physicists use models for a variety of purposes. For example, models can help physicists analyze a scenario and perform a calculation, or they can be used to represent a situation in the form of a computer simulation. A theory is an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers. Some theories include models to help visualize phenomena, whereas others do not. Newton’s theory of gravity, for example, does not require a model or mental image, because we can observe the objects directly with our own senses. The kinetic theory of gases, on the other hand, is a model in which a gas is viewed as being composed of atoms and molecules. Atoms and molecules are too small to be observed directly with our senses—thus, we picture them mentally to understand what our instruments tell us about the behavior of gases.

A law uses concise language to describe a generalized pattern in nature that is supported by scientific evidence and repeated experiments. Often, a law can be expressed in the form of a single mathematical equation. Laws and theories are similar in that they are both scientific statements that result from a tested hypothesis and are supported by scientific evidence. However, the designation law is reserved for a concise and very general statement that describes phenomena in nature, such as the law that energy is conserved during any process, or Newton’s second law of motion, which relates force, mass, and acceleration by the simple equation F = m a F = m a . A theory, in contrast, is a less concise statement of observed phenomena. For example, the Theory of Evolution and the Theory of Relativity cannot be expressed concisely enough to be considered a law. The biggest difference between a law and a theory is that a theory is much more complex and dynamic. A law describes a single action, whereas a theory explains an entire group of related phenomena. And, whereas a law is a postulate that forms the foundation of the scientific method, a theory is the end result of that process.

Less broadly applicable statements are usually called principles (such as Pascal’s principle, which is applicable only in fluids), but the distinction between laws and principles often is not carefully made.

Models, Theories, and Laws

Models, theories, and laws are used to help scientists analyze the data they have already collected. However, often after a model, theory, or law has been developed, it points scientists toward new discoveries they would not otherwise have made.

The models, theories, and laws we devise sometimes imply the existence of objects or phenomena as yet unobserved. These predictions are remarkable triumphs and tributes to the power of science. It is the underlying order in the universe that enables scientists to make such spectacular predictions. However, if experiment does not verify our predictions, then the theory or law is wrong, no matter how elegant or convenient it is. Laws can never be known with absolute certainty because it is impossible to perform every imaginable experiment in order to confirm a law in every possible scenario. Physicists operate under the assumption that all scientific laws and theories are valid until a counterexample is observed. If a good-quality, verifiable experiment contradicts a well-established law, then the law must be modified or overthrown completely.

The study of science in general and physics in particular is an adventure much like the exploration of uncharted ocean. Discoveries are made; models, theories, and laws are formulated; and the beauty of the physical universe is made more sublime for the insights gained.

The Scientific Method

Ibn al-Haytham (sometimes referred to as Alhazen), a 10th-11th century scientist working in Cairo, significantly advanced the understanding of optics and vision. But his contributions go much further. In demonstrating that previous approaches were incorrect, he emphasized that scientists must be ready to reject existing knowledge and become "the enemy" of everything they read; he expressed that scientists must trust only objective evidence. Al-Haytham emphasized repeated experimentation and validation, and acknowledged that senses and predisposition could lead to poor conclusions. His work was a precursor to the scientific method that we use today.

As scientists inquire and gather information about the world, they follow a process called the scientific method . This process typically begins with an observation and question that the scientist will research. Next, the scientist typically performs some research about the topic and then devises a hypothesis. Then, the scientist will test the hypothesis by performing an experiment. Finally, the scientist analyzes the results of the experiment and draws a conclusion. Note that the scientific method can be applied to many situations that are not limited to science, and this method can be modified to suit the situation.

Consider an example. Let us say that you try to turn on your car, but it will not start. You undoubtedly wonder: Why will the car not start? You can follow a scientific method to answer this question. First off, you may perform some research to determine a variety of reasons why the car will not start. Next, you will state a hypothesis. For example, you may believe that the car is not starting because it has no engine oil. To test this, you open the hood of the car and examine the oil level. You observe that the oil is at an acceptable level, and you thus conclude that the oil level is not contributing to your car issue. To troubleshoot the issue further, you may devise a new hypothesis to test and then repeat the process again.

The Evolution of Natural Philosophy into Modern Physics

Physics was not always a separate and distinct discipline. It remains connected to other sciences to this day. The word physics comes from Greek, meaning nature. The study of nature came to be called “natural philosophy.” From ancient times through the Renaissance, natural philosophy encompassed many fields, including astronomy, biology, chemistry, physics, mathematics, and medicine. Over the last few centuries, the growth of knowledge has resulted in ever-increasing specialization and branching of natural philosophy into separate fields, with physics retaining the most basic facets. (See Figure 1.11 , Figure 1.12 , and Figure 1.13 .) Physics as it developed from the Renaissance to the end of the 19th century is called classical physics . It was transformed into modern physics by revolutionary discoveries made starting at the beginning of the 20th century.

Classical physics is not an exact description of the universe, but it is an excellent approximation under the following conditions: Matter must be moving at speeds less than about 1% of the speed of light, the objects dealt with must be large enough to be seen with a microscope, and only weak gravitational fields, such as the field generated by the Earth, can be involved. Because humans live under such circumstances, classical physics seems intuitively reasonable, while many aspects of modern physics seem bizarre. This is why models are so useful in modern physics—they let us conceptualize phenomena we do not ordinarily experience. We can relate to models in human terms and visualize what happens when objects move at high speeds or imagine what objects too small to observe with our senses might be like. For example, we can understand an atom’s properties because we can picture it in our minds, although we have never seen an atom with our eyes. New tools, of course, allow us to better picture phenomena we cannot see. In fact, new instrumentation has allowed us in recent years to actually “picture” the atom.

Limits on the Laws of Classical Physics

For the laws of classical physics to apply, the following criteria must be met: Matter must be moving at speeds less than about 1% of the speed of light, the objects dealt with must be large enough to be seen with a microscope, and only weak gravitational fields (such as the field generated by the Earth) can be involved.

Some of the most spectacular advances in science have been made in modern physics. Many of the laws of classical physics have been modified or rejected, and revolutionary changes in technology, society, and our view of the universe have resulted. Like science fiction, modern physics is filled with fascinating objects beyond our normal experiences, but it has the advantage over science fiction of being very real. Why, then, is the majority of this text devoted to topics of classical physics? There are two main reasons: Classical physics gives an extremely accurate description of the universe under a wide range of everyday circumstances, and knowledge of classical physics is necessary to understand modern physics.

Modern physics itself consists of the two revolutionary theories, relativity and quantum mechanics. These theories deal with the very fast and the very small, respectively. Relativity must be used whenever an object is traveling at greater than about 1% of the speed of light or experiences a strong gravitational field such as that near the Sun. Quantum mechanics must be used for objects smaller than can be seen with a microscope. The combination of these two theories is relativistic quantum mechanics, and it describes the behavior of small objects traveling at high speeds or experiencing a strong gravitational field. Relativistic quantum mechanics is the best universally applicable theory we have. Because of its mathematical complexity, it is used only when necessary, and the other theories are used whenever they will produce sufficiently accurate results. We will find, however, that we can do a great deal of modern physics with the algebra and trigonometry used in this text.

Check Your Understanding

A friend tells you they have learned about a new law of nature. What can you know about the information even before your friend describes the law? How would the information be different if your friend told you they had learned about a scientific theory rather than a law?

Without knowing the details of the law, you can still infer that the information your friend has learned conforms to the requirements of all laws of nature: it will be a concise description of the universe around us; a statement of the underlying rules that all natural processes follow. If the information had been a theory, you would be able to infer that the information will be a large-scale, broadly applicable generalization.

PhET Explorations

Equation grapher.

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y = bx y = bx ) to see how they add to generate the polynomial curve.

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  • Authors: Paul Peter Urone, Roger Hinrichs
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  • Book title: College Physics 2e
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The Science of Physics

Chapter Overview

  • Nature of physics and its related fields
  • Scientific method of inquiry
  • Role of models
  • Basic SI units
  • Precision vs. accuracy
  • Scientific notation
  • Significant digits
  • Various ways of summarizing data
  • Dimensional analysis
  • Estimation procedures

Section 1.1 What is Physics?

  • Identify activities and fields that involve the major areas within physics
  • Describe the processes of the scientific method
  • Describe the role of models and diagrams in physics

1.1 What is Physics?

  • The study of the physical world
  • Use a small number of basic concepts, equations, and assumptions to describe the physical world
  • Can be used to make predictions about a broad range of phenomena
  • Appliances, tools, buildings, inventions are all basic physics principles put to test

Thermodynamics – Efficient engines, use of coolants

Electromagnetism – Battery, starter, headlights

Optics – Headlights, rearview mirrors

Vibrations and mechanical waves – Shock absorbers, radio speakers, sound insulation

Mechanics – spinning motion of the wheels, tires that provide enough friction or traction

Physics is Everywhere

  • When you buy ice cream, why do you put it in the freezer when you get home?
  • **Any problem that deals with temperature, size, motion, position, shape, or color involves physics**
  • There are major areas of physics that deal with each of these
  • Design, build, and operate
  • Best shape so that is remains stable and floating, yet quick and maneuverable
  • Knowledge of fluids
  • Efficient shape for sails and how to arrange them
  • Understanding motion and its causes
  • Balancing loads
  • So port isn't heavier than starboard
  • Knowledge on how the keel keeps the boat moving in one direction
  • Even though the wind i s blowing in another

The Scientific Method

  • No single procedure is always taken in an experiment
  • Certain common steps in all good scientific investigations
  • There was a car accident and the police were investigating… use the scientific method:
  • Observations/Data:
  • Hypothesis:
  • Experiments/Tests:
  • Interpret/Revise Hypothesis:
  • Conclusion:
  • Simple models are often used to explain the most fundamental features of various phenomena
  • Common technique
  • Break an event down into different parts
  • Use a model for each section

WE WILL ALWAYS DRAW

MODELS!!!!!!

  • Observations
  • Ball’s size, spin, weight, color, surroundings, time in the air, speed, and sound when hitting ground
  • Identify the system
  • A single object and the items immediately affecting it
  • Ball and its motion
  • Disregard any characteristics that don't matter
  • Color, sound when hitting the ground
  • In some studies of motion, even size and spin are disregarded

Models Help Build Hypothesis

  • A hypothesis is a reasonable explanation for observations
  • Can be tested with additional experiments
  • Modeling a situation can help identify variables as well
  • Galileo’s ‘thought experiment’

Models Help Guide Experiments

  • Galileo performed many experiments
  • Observing weight only
  • Used same size objects, just different weight
  • No way to eliminate air resistance
  • Used rolling ball down smooth ramps as a model
  • The steeper the ramp, the closer the representation

Experiments

  • Must deal with variables
  • Majority of the time a controlled experiment
  • Only one variable changed at a time
  • Used same set of different weight balls
  • Just down a steeper ramp each time

Hypothesis to Prediction

  • Until the invention of the air pump, it was impossible to perform direct tests in the absence of air resistance
  • Reasonably accurate predictions were still made
  • Experiments are run until results match each other and are in agreement with the hypothesis
  • If not there could be error
  • Then the hypothesis must be revised
  • Conclusions
  • Are only valid if they can be duplicated and verified by other people under the same conditions
  • Not only so scientists conduct experiments to test hypothesis
  • They also RESEARCH!!!
  • Steps to doing scientific research
  • Identifying reliable resources
  • Searching the sources to find references
  • Checking carefully for opposing views
  • Documenting sources
  • Presenting findings to other scientists for review and discussion

Section 1.2 Measurements In Experiments

  • List basic SI units and the quantities they describe
  • Convert measurements into scientific notation
  • Distinguish between accuracy and precision
  • Use significant figures in measurements and calculations

Numbers as Measurements

  • When in physics numbers will never stand alone
  • Means absolutely nothing
  • Must have units following the number
  • (anything labeled without units will be wrong) ☺
  • Length, mass, time, or something else?
  • If length: inches, centimeters, kilometers, l ight-years?
  • The units helps tell us what kind of physical quantity being measured
  • Basic dimensions – length, mass, time
  • There are many other dimensions as well
  • Force, velocity , energy, volume, and acceleration
  • All combinations of length, mass, and time
  • SI is the standard measurement system for science
  • Scientists like to use the same system of units for measurement
  • If not that would be a lot of converting ☹
  • 7 base units that each describe a single dimension
  • Length – meters (m)
  • Mass – grams (g)
  • Time – seconds (s)
  • Other units derived from the 3 bases

SI Prefixes

  • A very wide range of measurements will be used
  • 100,000,000,000,000,000 m for distances between stars
  • .000 000 001 m distances between atoms in a solid
  • Can deal with powers of ten
  • Prefixes to go with the powers

Conversions

  • Using SI, with the prefixes and same base
  • Conversion factors will always = 1
  • Any measurement multiplied by a fraction will be multiplied by 1
  • The number and unit will change but the quantity will stay the same

Dimensional Analysis

  • Mathematical techniques that uses conversion factors to convert from one unit to another
  • A typical bacterium has a mass of about 2.0μg. Express this in terms of grams and kilograms.
  • The mass of an average person is 60,000,000 mg. Express this in grams and kilograms.

Dimension and Units Must Agree

  • Can’t measure a length then label in kilograms (kg)
  • Must make sure use correct unit
  • We will ALWAYS use metric!!
  • No inches, feet, miles, lbs, tons

Accuracy and Precision

  • The closeness of measurements to the correct or accepted value
  • Closeness of a set of measurements of the same quantity made in the same way

Accepted Value = 55 km/h

Problems with Accuracy are Due to Error

  • Experimental work is never free of error
  • Important to minimize as much as possible
  • Should never have human error
  • Mistake in reading measurement
  • Mistake in recording results
  • Method should always be the same
  • Same instrument
  • Check calculations

Precision of Instrument

  • Poor accuracy can be corrected
  • Precision based on the instrument
  • Instruments can only be so precise

Precise to the .1

Estimate the last place

Significant Figures

  • Measurement that consists of all known digits with an uncertain digit at the end
  • Uncertain digit
  • The digit that you as the experimenter must estimate
  • All digits are significant, but not necessarily certain
  • Insignificant digits are never reported
  • YOU WILL ALWAYS NEED TO USE SIGNIFICANT FIGURES!!!!!

Sig Fig Rules

Sample Problems

  • How many significant figures?
  • Always round to significant figures
  • If adding 2 numbers with 3 significant figures each
  • Answer will have 3 significant figures
  • Use normal rounding
  • 5 and up – round up
  • 4 and down – stay the same

Sig Fig Math

  • Adding and Subtracting
  • Answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.
  • 2.59 + 6.8974 = 9.49
  • Multiplying and Dividing
  • Answer can have no more significant figures than are in the measurement with the fewest number of significant figures.
  • 3.05/8.47 = .360

Practice Problems

  • 5.44m – 2.6103m =
  • 2.4g/mL x 15.82 mL =

Conversion Factors and Sig Figs

  • Because a measurement is considered exact, after conversion there is no rounding

Section 1.3 The Language of Physics

  • Interpret data in tables and graphs, and recognize equations that summarize data
  • Distinguish between conventions for abbreviating units and quantities
  • Use dimensional analysis to check the validity of expressions
  • Perform order of magnitude calculations

Mathematics and Physics

  • Tools are used to summarize and analyze data and observations
  • Often times mathematical relationships
  • In forms of charts and graphs
  • Provides a visual of time versus distance
  • Can determine distance traveled at any time
  • Through this equation

(change in position m) = 4.9 x (time of fall s) 2

  • How far would the ball have fallen at .500 s?

Equations Indicate Relationships

  • Equations show how two or more variables are related
  • Many equations do not have numbers
  • But symbols representing physical constants
  • Δ means difference or change in
  • Usually final minus initial
  • Units should help with equations
  • Units must cancel correctly
  • Want the units that match your answer
  • If finding velocity should end with units of m/s

Units or Variables?

  • Variables are usually boldface
  • Stand for a measurement with specific units
  • Always check the context of the problem
  • Find the mass of something
  • Mass is variable m, units would be g or kg
  • Examples of Variables
  • Δx, Δy, Δt, c, m, a, v
  • Examples of Units
  • m, kg, m/s, m/s 2 , s
  • Use to check validity of equations
  • A car is moving at a speed of 88 km/h and has traveled 725 km, how long did this trip take?

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Physics library

Unit 1: one-dimensional motion, unit 2: two-dimensional motion, unit 3: forces and newton's laws of motion, unit 4: centripetal force and gravitation, unit 5: work and energy, unit 6: impacts and linear momentum, unit 7: torque and angular momentum, unit 8: oscillations and mechanical waves, unit 9: fluids, unit 10: thermodynamics, unit 11: electric charge, field, and potential, unit 12: circuits, unit 13: magnetic forces, magnetic fields, and faraday's law, unit 14: electromagnetic waves and interference, unit 15: geometric optics, unit 16: special relativity, unit 17: quantum physics, unit 18: discoveries and projects, unit 19: review for ap physics 1 exam.

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Free Physics PowerPoint Template and Google Slides

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The templates of Physics are eye-catching layouts of scientific experiments and theories. These Physics PowerPoint Templates are suitable for academic purposes. Because the slides show a colorful illustration of chemical reactions are components that can simulation-based learning and teaching. The PowerPoint templates of Physics also useful for presenting multiple categories of natural science. These may include time & relativity, quantum mechanics wave motions, etc. Here, PowerPoint shapes present global metaphors for scientific tools such as lab equipment and convergence models. The editable presentations of science and physics can change colors from solid fill and theme options.

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Top 101 Physics Topics For Presentation [Updated]

physics topics for presentation

Physics, the science that seeks to understand the fundamental principles governing the universe, offers a vast array of intriguing topics suitable for presentations. From classical mechanics to quantum physics, the realm of physics encompasses a wide range of phenomena that shape our understanding of the natural world. In this blog, we’ll delve into various physics topics for presentations, exploring their significance, applications, and relevance in everyday life.

How to Make Your Physics Presentation?

Table of Contents

Creating a compelling physics presentation involves careful planning, research, and effective communication of complex concepts in a clear and engaging manner. Here are some steps to help you make your physics presentation:

  • Choose a Topic: Select a physics topic that interests you and aligns with your audience’s level of understanding. Consider the relevance and significance of the topic and its potential to engage and educate your audience.
  • Conduct Research: Research thoroughly using trusted sources like textbooks, scientific journals, and reputable websites to grasp the topic’s key concepts.
  • Develop an Outline: Organize your presentation into logical sections or themes. Use the outline provided earlier as a template, adapting it to suit your chosen topic and presentation format.
  • Create Visual Aids: Prepare visual aids such as slides, diagrams, and animations to complement your presentation. Use clear and concise graphics to illustrate complex concepts and enhance audience comprehension.
  • Craft a Clear Narrative: Structure your presentation with a clear beginning, middle, and end. Start with an attention-grabbing introduction to introduce the topic and establish its relevance. Present the main content in a logical sequence, highlighting key points and supporting evidence. Conclude with a summary of key takeaways and implications.
  • Practice Delivery: Rehearse your presentation multiple times to familiarize yourself with the content and refine your delivery. Pay attention to pacing, clarity, and nonverbal communication cues such as posture and gestures.
  • Engage Your Audience: Encourage active participation and interaction by asking questions, soliciting feedback, and incorporating interactive elements such as demonstrations or group activities. Tailor your presentation to the interests and background knowledge of your audience to keep them engaged and attentive.
  • Anticipate Questions: Prepare for potential questions from your audience by anticipating areas of confusion or ambiguity in your presentation. Be ready to provide clarifications, examples, or references to further resources to address any inquiries.
  • Seek Feedback: Solicit feedback from peers, mentors, or colleagues to gain valuable insights into areas for improvement. Consider their suggestions and incorporate constructive criticism to enhance the effectiveness of your presentation.
  • Reflect and Iterate: After delivering your presentation, take time to reflect on your performance and the audience’s response. Identify strengths and weaknesses, and consider how you can refine your approach for future presentations.

By following these steps and applying careful planning and preparation, you can create a compelling physics presentation that effectively communicates complex concepts and engages your audience in the wonders of the natural world.

Top 101 Physics Topics For Presentation

  • Newton’s Laws of Motion
  • Conservation of Energy
  • Conservation of Momentum
  • Projectile Motion
  • Friction: Types and Effects
  • Laws of Thermodynamics
  • Heat Transfer Mechanisms
  • Applications of Thermodynamics
  • Electric Fields and Charges
  • Magnetic Fields and Forces
  • Electromagnetic Induction
  • Applications of Electricity and Magnetism
  • Reflection and Refraction of Light
  • Wave Optics and Interference
  • Optical Instruments: Microscopes and Telescopes
  • Modern Optical Technologies
  • Wave-Particle Duality
  • Heisenberg’s Uncertainty Principle
  • Quantum Tunneling
  • Applications of Quantum Mechanics
  • Special Theory of Relativity
  • General Theory of Relativity
  • Time Dilation and Length Contraction
  • Black Holes: Formation and Properties
  • Dark Matter and Dark Energy
  • Atomic Structure and Spectroscopy
  • Radioactivity and Nuclear Reactions
  • Nuclear Energy: Pros and Cons
  • Nuclear Medicine: Applications and Techniques
  • Stars: Formation and Evolution
  • Stellar Structure and Dynamics
  • Galaxies: Types and Properties
  • Cosmology: The Big Bang Theory
  • Gravitational Waves: Detection and Significance
  • Quantum Gravity: Theoretical Concepts
  • String Theory: Basics and Implications
  • High Energy Physics: Particle Accelerators
  • Standard Model of Particle Physics
  • Quantum Field Theory
  • Symmetry in Physics
  • Chaos Theory: Deterministic Chaos
  • Fluid Dynamics: Flow Patterns and Applications
  • Aerodynamics: Principles and Applications
  • Bernoulli’s Principle
  • Newtonian and Non-Newtonian Fluids
  • Quantum Computing: Principles and Applications
  • Cryptography: Quantum Key Distribution
  • Quantum Teleportation
  • Quantum Entanglement
  • Bose-Einstein Condensate
  • Superconductivity: Phenomena and Applications
  • Magnetic Levitation: Maglev Trains
  • Quantum Dots: Properties and Uses
  • Nanotechnology: Applications in Physics
  • Carbon Nanotubes: Structure and Properties
  • Graphene: Properties and Potential Applications
  • Optoelectronics: Devices and Technologies
  • Photonics: Light-based Technologies
  • Lasers: Principles and Applications
  • Holography: 3D Imaging Techniques
  • Quantum Sensors: Principles and Applications
  • Quantum Metrology: Precision Measurements
  • Quantum Biology: Biological Processes from a Quantum Perspective
  • Quantum Optics: Manipulation of Light at the Quantum Level
  • Quantum Materials: Properties and Potential Applications
  • Quantum Algorithms: Computational Advantages of Quantum Computing
  • Topological Insulators: Unique Electronic Properties
  • Neutrinos: Properties and Detection
  • Neutron Stars and Pulsars
  • Magnetars: Extremely Magnetic Neutron Stars
  • Cosmic Rays: Origins and Effects
  • Solar Physics: Sunspots and Solar Flares
  • Aurora Borealis and Aurora Australis
  • Space Weather: Impact on Earth and Satellites
  • Plasma Physics: Properties and Applications
  • Fusion Energy: Achievements and Challenges
  • Particle Astrophysics: Cosmic Rays and High-Energy Particles
  • Quantum Astrophysics: Applying Quantum Mechanics to Cosmological Phenomena
  • Exoplanets: Discoveries and Characterization
  • Astrobiology: Search for Extraterrestrial Life
  • Cosmic Microwave Background Radiation
  • Black Hole Thermodynamics
  • Gravitational Lensing: Observational Effects
  • Multiverse Theory: Theoretical Implications of Cosmology
  • Quantum Consciousness: Theoretical Considerations
  • Quantum Gravity: Unifying Quantum Mechanics and General Relativity
  • Quantum Cosmology: Cosmological Models Based on Quantum Theory
  • Quantum Field Theory: Foundations and Applications in Particle Physics
  • Quantum Gravity: Approaches and Challenges
  • Quantum Chromodynamics: Theory of Strong Interactions
  • Quantum Electrodynamics: Theory of Electromagnetic Interactions
  • Quantum Spin: Properties and Applications
  • Quantum Hall Effect: Topological Phenomenon in Condensed Matter Physics
  • Quantum Phase Transitions: Critical Phenomena in Quantum Systems
  • Quantum Computing: Architectures and Algorithms
  • Quantum Communication: Secure Communication Based on Quantum Principles
  • Quantum Simulation: Modeling Complex Quantum Systems
  • Quantum Cryptography : Secure Communication Using Quantum Key Distribution
  • Quantum Sensing: Ultra-Precise Measurement Techniques
  • Quantum Metrology: Achieving High Precision with Quantum Techniques
  • Quantum Technologies: Emerging Applications of Quantum Physics

Tips to Fellow to Make Physics Presentation Successful

Making a physics presentation successful requires careful planning, effective communication, and engaging presentation skills. Here are some tips to help your fellow make their physics presentation successful:

  • Know Your Audience: Understand the background knowledge and interests of your audience to tailor your presentation accordingly. Adjust the level of technical detail and terminology to ensure clarity and engagement.
  • Define Clear Objectives: Clearly define the objectives of your presentation, outlining what you aim to achieve and the key points you intend to convey. This will help you stay focused and ensure that your presentation delivers a coherent message.
  • Organize Your Content: Structure your presentation in a logical manner, with a clear introduction, main body, and conclusion. Use headings, subheadings, and bullet points to organize your content and guide the audience through your presentation.
  • Use Visual Aids Wisely: Incorporate visual aids such as slides, diagrams, and animations to enhance understanding and retention of key concepts. Keep visual elements clear, concise, and relevant to the content of your presentation.
  • Practice Delivery: Rehearse your presentation multiple times to familiarize yourself with the content and refine your delivery. Pay attention to pacing, tone of voice, and body language to ensure confident and engaging presentation delivery.
  • Engage Your Audience: Encourage active participation and interaction by asking questions, soliciting feedback, and incorporating interactive elements such as demonstrations or group activities. Engage with your audience to maintain their interest and attention throughout your presentation.
  • Clarify Complex Concepts: Break down complex concepts into simpler, more understandable terms, using analogies, examples, and real-world applications to illustrate key points. Clarify any technical jargon or terminology to ensure that all audience members can follow along.
  • Be Prepared for Questions: Anticipate questions from your audience and prepare thoughtful responses in advance. Be open to feedback and willing to address any uncertainties or misconceptions that may arise during the Q&A session.
  • Demonstrate Enthusiasm: Convey your passion and enthusiasm for the subject matter through your presentation delivery. Demonstrate genuine interest and excitement in sharing your knowledge with your audience, inspiring curiosity and engagement.
  • Seek Feedback: After delivering your presentation, solicit feedback from your audience and peers to gain valuable insights into areas for improvement. Reflect on their input and incorporate constructive criticism to enhance the effectiveness of your future presentations.

Physics is fascinating! It’s like a colorful quilt filled with amazing ideas and things that make us wonder about the universe. Whether we’re talking about basic stuff like how things move or super cool things like quantum mechanics, physics presentations help us understand how the world works. They show us the important rules that make everything tick, from tiny atoms to huge galaxies.

By learning about physics, we can see how clever humans are in figuring out nature’s secrets and using them to make awesome technology. It’s like unlocking a treasure chest full of wonders and surprises!

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Physics powerpoint presentations free to download and use for teaching.

Using PowerPoint for teaching physics can be an effective way to engage your students and present complex concepts visually. Here are some tips on how to use PowerPoint effectively for teaching physics:

Start with an outline: Plan your presentation by creating an outline that outlines the main topics and subtopics you want to cover. This will help you organize your content and ensure a logical flow.

Use visuals: Physics often involves abstract concepts that can be challenging for students to grasp. Incorporate relevant visuals such as diagrams, graphs, images, or videos to make the concepts more tangible and easier to understand.

Simplify complex ideas: Break down complex physics concepts into smaller, more digestible pieces. Use step-by-step explanations and visual representations to help students follow along and grasp the core principles.

Use animations and transitions: PowerPoint offers animation and transition features that can be used to demonstrate processes or show how variables change over time. For example, you can use animations to illustrate the motion of objects or the behavior of waves

Below are a list of physics powerpoint presentations.

These have been submitted by teachers to help other teachers. They can be used freely and modified to your own preferred format.

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Other hints and tips for making physics powerpoint presentations

Incorporate real-world examples: Relate physics concepts to real-life examples and applications. Show how these concepts are used in everyday situations or in specific fields like engineering or astronomy. This can help students connect theory to practical applications.

Encourage active learning: Design interactive slides that encourage student participation. Include questions, quizzes, or problem-solving activities within your presentation. This promotes active engagement and helps students apply their knowledge.

Provide clear explanations: Use concise and clear explanations to convey information. Break down complex equations or formulas into smaller parts and explain each component separately. Use bullet points, charts, or diagrams to support your explanations.

Include practice problems: Dedicate slides to practice problems that allow students to apply the concepts they have learned. Walk them through the problem-solving process step by step and provide explanations for each step.

Allow for discussion and questions: Allocate time for students to ask questions or engage in discussions related to the presented material. Encourage active participation and create a supportive learning environment.

Keep it visually appealing: Use a consistent and visually appealing design throughout your presentation. Choose an appropriate font, color scheme, and layout that is easy to read and visually appealing. Avoid cluttered slides that may distract or confuse students.

Use multimedia elements: Consider incorporating videos, simulations, or interactive online resources to enhance student understanding and engagement. These can provide visual demonstrations or virtual experiments that supplement your teaching.

Review and summarize: End your presentation with a summary slide that recaps the main points covered. Reinforce key concepts and encourage students to review the material on their own.

Remember to adapt your presentation style to suit the needs of your students and adjust the pace of your presentation accordingly. Be prepared to answer questions and provide further clarification as needed.

Topics For Seminar

200 Interesting Physics Seminar and Powerpoint Presentation Topics

interesting topics for powerpoint presentation physics

Interesting topics for Powerpoint Presentation in Physics

  • Special Relativity and General Relativity
  • Quantum Computing
  • Time dilation
  • Physics of Babies
  • Nikola Tesla Inventions  ( PPT2 )
  • Greatest Physicists and their contribution
  • Physics-Chemistry-Biology Relation
  • Physics in Sports   Link 2
  • Physics in our everyday life
  • Newtonian and Non-newtonian fluid
  • Anti-Gravity
  • Thermodynamics in Everyday Life
  • Airborne Wind Energy / Flying Windmills
  • Pumped-storage hydroelectricity
  • Compressed air energy storage  ( PDF )
  • Magnetoresistance
  • Fusion Power Generation
  • Fluid Flow Continuity and Bernoulli’s Equation
  • Archimedes' Principle  and Its Applications
  • Physics of Touch Screens Technology  ( Article )
  • Exoplanets / Extra-Solar Planets
  • Space Telescopes ( Hubble / James Webb Space Telescope )
  • Carbon Nanotubes
  • The Physics of the Egyptian Pyramids
  • Magnus effect and its applications
  • Sustainable energy  ( PPT 2 )
  • The Physics of Fire  ( PPT )
  • The Motion of the Planets
  • Artificial Intelligence (AI) in Our Everyday Life
  • The String theory: A theory of Everything
  • Electromagnetism  and Its applications in daily life
  • Electromagnetic Induction
  • Electromagnetic Spectrum  / Electromagnetic Radiation
  • Transformers
  • Force sensor
  • Friction in our everyday life and Its types  ( PPT 2 ) ( PDF )
  • Magnetorheological fluid
  • Magnetic field due to currents in wires  ( PPT 2 )
  • Magnetic field patterns
  • Earth's Magnetic Field
  • Searching for Magnetic Monopoles
  • Electricity and Magnetism
  • Maglev Trains: Transrapid magnetic lift trains
  • Magnetic Levitation
  • Microwave Oven: How it works? ( PDF Report )
  • Physics Behind the Climate Change ( PDF Report )
  • Electromagnets and their uses
  • Fresnel's Equations
  • Electric Potential
  • Working of Motors
  • Working of Generators
  • Bioelectromagnetism
  • Kinematics in our daily lives
  • Real-Life Examples of Newton’s First Law (Inertia)
  • Zero Energy Buildings
  • Lightning Bolt Physics
  • Lightning Protection System  (Static Electricity)
  • Electromagnetic Railguns
  • Physics behind fidget spinner
  • Hoverboard (Self-balancing scooter)
  • Physics of roller coasters
  • Physics behind musical instruments
  • Physics Behind Bruce Lee's One-Inch Punch!
  • Electric Cars
  • Working with simple electrical components
  • Current and charge
  • Ohm's law and resistance
  • Oscilloscope
  • String theory
  • Resistance effects
  • Electrical conduction through gases
  • Electrostatic charges
  • Van de Graaff generator
  • Energy conversion
  • Components of motion
  • Circular motion
  • Weightlessness
  • Forced vibrations and resonance
  • Momentum in two dimensions
  • Simple harmonic motion
  • Fiction and Its types
  • Friction at the atomic level
  • Coulomb model
  • Superfluidity
  • Transmission Lines
  • Peso Electricity
  • Atmospheric Optics
  • Wireless Electricity
  • Models of electric circuits
  • Wind Energy
  • Solar Power
  • Geothermal Energy
  • Wave Energy
  • Concentrated Solar Energy
  • Nuclear Power Generation
  • Physics behind the Aurora Borealis
  • Plasma Physics
  • Particle Detectors, Drift Chambers
  • Exponential decay and half-life
  • Nuclear Fission
  • Nuclear Fusion
  • Biogas Plant
  • Biomass Energy
  • First models of the atom
  • Cloud chambers
  • Particle Accelerators
  • Synchrotron
  • Model of the atom
  • Light behaving like a particle
  • Electrons behaving as waves
  • Evidence for the hollow atom
  • Nature of ionizing radiations
  • Radioactive sources: isotopes and availability
  • Acceleration due to gravity
  • Radio Waves
  • Antenna Theory and Design
  • How do Mobile networks work?
  • Solar System
  • Asteroid Belt Formation
  • Satellite Communication
  • Possibility of life on Mars
  • Mangalyaan (India's Mars Mission)
  • Chandrayaan-I (India's Lunar Mission)
  • Rocket Technology
  • Satellite Launch Vehicles
  • SpaceX: Falcon Heavy
  • Reusable Rockets
  • Space Organisations and their achievements
  • Global Navigation Satellite System 
  • Gravitational force and free fall
  • Radar Technologies
  • Newtonian fluid
  • Pinhole camera and lens camera
  • Diffraction of light
  • Reflection of light
  • Refraction of light
  • Radio Telescope
  • Formation of Galaxies
  • Hubble's Law (Evidence)
  • Gravity waves
  • Kepler’s laws
  • The Copernican revolution
  • Magnetic sail
  • Planetary motion and gravity
  • Big Bang (The Origin)
  • Beyond Solar System
  • Constellations
  • Life on Mars
  • Mars Exploration
  • Why is Venus So Hot?
  • Trans-Neptunian region
  • Space-Time Fabric
  • Journey of Photons
  • Atmospheric pressure
  • Einstein's Theory of Relativity
  • How do airplanes fly?
  • Aerodynamics
  • Types of waves
  • Young's slits
  • Superconductivity
  • LED | OLED | MicroLED
  • Thermal radiation from the human body
  • Thermal expansion of Solid and Liquid
  • Concept of density
  • Evidence for atoms
  • Molecular speed
  • Higgs boson
  • Chandrashekar limit
  • Nuclear Reactors
  • Large Hadron Collider
  • Quantum Mechanics (Introduction)
  • Young's double-slit experiment
  • Doppler effect in Sound
  • Doppler effect in Light
  • Integrated Circuits
  • Microprocessors
  • Display Technology
  • 3D Printing
  • Virtual Reality
  • Biosensors and Bioelectronics
  • Ambient intelligence
  • Storage Devices
  • Semiconductors
  • Fiber-optic communication
  • Three Phase Circuit
  • Home's electrical system
  • Types of Gear and working
  • Electric Bill Calculation
  • Impulse, Momentum, and Collisions
  • Dark Energy (Quantum Vacuum Energy) 
  • Dark Matter
  • Acoustic Levitator
  • Electrometer
  • Hydroelectricity
  • Optical instruments

Interesting Questions for Physics Powerpoint Presentation Ideas

  • Why do things move?
  • Does everything that goes up come down?
  • Why does a bicycle stay upright when it's moving but fall when it stops?
  • Why do we wear seatbelts?
  • Why doesn’t the moon fall into the earth?
  • Why is it tough to walk on ice?
  • Why does ice melt?
  • Why doesn’t the moon fall?
  • What is sound?
  • What is light?
  • What is lightning?
  • What makes rainbows?
  • How can a boat make of steel float?
  • Why can’t we see air, how do we know that it's there?
  • Why are some turns on roads banked?  
  • What keeps me from falling on the Silly  Silo at Adventureland?
  • Why do my socks sometimes stick together in the clothes dryer?
  • Why do I get a shock after I walk across the carpet room and touch something in winter? 
  • What’s the deal with magnets? Why do they stick on refrigerators?
  • By the way, how do refrigerators and air conditioners work?
  • Why can’t I cool my room by keeping the refrigerator door opened?
  • Why is it a bad idea to plug my TV,  stereo, computer, radio, and hairdryer into the same outlet?
  • Where does electricity come from?
  • Why doesn’t the electricity leak out of the outlet?
  • What do airplanes and curveballs have in common?
  • Why do my ears pop when I’m on a  plane?
  • Why can I see all of myself in a mirror that is half as tall as I am?
  • what is the Greenhouse effect?
  • what’s the deal with the ozone layer?
  • Is climate change real? Are we causing it? 
  • How do(es) x-rays, microwaves, ultrasound, MRIs, LASERS, and cable TV work.?
  • By the way, how does TV work?
  • Why does the water in my tub spin in a circle as it goes down the drain? Why does it always spin in the same direction? 
  • How does soap work?
  • Why is the sky blue during the day but red at sunset?
  • Are nuclear power plants safe?
  • How do they take my temperature by sticking that gadget into my ear?
  • Why does the cue ball stop dead when it hits another ball head-on?
  • What is a day, month, or year?
  • Why does a year on Jupiter last 12 years?
  • Are hydrogen fuel cells or hybrid cars the answer to the energy crisis?
  • What does it take to make an atomic bomb?

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Physics 11 Dynamics By: Bryon Long.

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Presentation on theme: "Physics 11 Dynamics By: Bryon Long."— Presentation transcript:

Physics 11 Dynamics By: Bryon Long

- Newton’s First and Second Laws - Gravity 3 - Newton’s Third Law

presentation physics

Newton’s Laws of Motion

presentation physics

Motion Notes Speed Momentum Acceleration and Force Friction and Air Resistance Newton’s Laws of Motion.

presentation physics

Aim: What is the law of conservation of momentum? Do Now: A 20 kg object traveling at 20 m/s stops in 6 s. What is the change in momentum? Δp = mΔv Δp.

presentation physics

Newton’s Laws.

presentation physics

Friction Gravity Newton’s Laws Momentum Forces.

presentation physics

Momentum and Collisions

presentation physics

Force A push or pull exerted on an object..

presentation physics

Forces and the Laws of Motion

presentation physics

Chapter 4 Dynamics: Newton’s Laws of Motion

presentation physics

Resistance of an object to a change in its motion inertia.

presentation physics

Forces & Newton’s Laws Ch. 4. Forces What is a force? –Push or pull one body exerts on another –Units = Newton (N) –Examples: List all of the forces that.

presentation physics

What is a Force? A force is a push or a pull causing a change in velocity or causing deformation.

presentation physics

Newton’s Laws of Motion 1 st - Inertia. 2 nd - F = ma 3 rd - Action/Reaction Take notes when see.

presentation physics

Sir Isaac Newton Newton’s Laws of Motion Newton’s 1st Law of Motion -An object at rest, will remain at rest, unless acted upon by an unbalanced.

presentation physics

Laws of Motion Forces: chapter st Law An object at rest remains at rest and an object in motion maintains its velocity unless it experiences an.

presentation physics

Chapters 5-6 Test Review Forces & Motion Forces  “a push or a pull”  A force can start an object in motion or change the motion of an object.  A force.

presentation physics

Newton’s Laws of Motion. Newton’s First Law  The Law of Inertia  Inertia- the tendency of an object to resist a change in motion.  An object at rest.

presentation physics

Energy Momentum, Collisions, Impulse. Momentum A measure of how hard it is to stop a moving object A measure of how hard it is to stop a moving object.

presentation physics

Forces, The laws of Motion & Momentum.

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Braid Group Action and Quasi-Split Affine \(\imath \) Quantum Groups II: Higher Rank

  • Published: 28 May 2024
  • Volume 405 , article number  142 , ( 2024 )

Cite this article

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  • Ming Lu 1 ,
  • Weiqiang Wang 2 &
  • Weinan Zhang 3  

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This paper studies quantum symmetric pairs \((\widetilde{\textbf{U}}, \widetilde{{\textbf{U}}}^\imath )\) associated with quasi-split Satake diagrams of affine type \(A_{2r-1}, D_r, E_{6}\) with a nontrivial diagram involution fixing the affine simple node. Various real and imaginary root vectors for the universal \(\imath \) quantum groups \(\widetilde{{\textbf{U}}}^\imath \) are constructed with the help of the relative braid group action, and they are used to construct affine rank one subalgebras of \(\widetilde{{\textbf{U}}}^\imath \) . We then establish relations among real and imaginary root vectors in different affine rank one subalgebras and use them to give a Drinfeld type presentation of \(\widetilde{{\textbf{U}}}^\imath \) .

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We thank the referees for very helpful comments and suggestions which improve the exposition of the paper. M.L. is partially supported by the National Natural Science Foundation of China (No. 12171333, 1226113149). W.W. and W.Z. are partially supported by the NSF grant DMS-2001351.

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Department of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China

Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, USA

Weiqiang Wang

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Proofs of Lemmas 3.2 and 3.6

In this appendix, we provide the detailed proofs for Lemma 3.2 and Lemma 3.6 .

1.1 Proof of Lemma  3.2

For convenience we recall Lemma  3.2 states that, for \(\tau i =i\in \mathbb {I}_0\) , we have

Let us verify the identity ( A.1 ).

We first recall several ingredients from [ WZ23 ], which will be used in the proof. Let \(\widetilde{\mathscr {T}}_i\) and \(\widetilde{\mathscr {T}}_w\) be the (rescaled) Lusztig braid group symmetries on \(\widetilde{\textbf{U}} \) introduced in [ WZ23 , §4.1]. Let \(\widetilde{ \Upsilon }\) be the quasi K -matrix for the quantum symmetric pair \((\widetilde{\textbf{U}} ,\widetilde{{\textbf{U}}}^\imath )\) and \(\widetilde{ \Upsilon }_i\) be rank one quasi K -matrices, for \(i\in \mathbb {I}\) . [ WZ23 , Theorem 3.6] is applicable to the \(\textbf{T}_i\) in Theorem  2.6 in the split affine type, and it gives us

for any \(x\in \widetilde{{\textbf{U}}}^\imath \) .

By assumption \(\tau i=i\) , we have \(\textbf{r}_i=s_i\) , \(t_{{\varpi }_i} =t_{\omega _i}\) and \(t_{{\varpi }_i'} =t_{\omega _i'}\) . Fix a reduced expression \(t_{\omega '_i} =\tau _i s_{i_1}s_{i_2} \cdots s_{i_k}\) where \(\tau _i\) is a Dynkin diagram automorphism. We define

( \(\widetilde{ \Upsilon }_{\omega '_i}\) here differs from the element in [ WZ23 , (8.1)] by the anti-involution \(\sigma \) . By [ WZ23 , Theorem 8.1] \(\widetilde{ \Upsilon }_{\omega '_i}\) is independent of the choice of a reduced expression of \(t_{\omega '_i}\) .) Then a repeated use of ( A.2 ) gives us

To verify ( A.1 ), we shall apply a strategy similar to [ WZ23 , Proof of Proposition 7.2] (where the notation \(\widetilde{\mathscr {T}}'_{w,-1} =\widetilde{\mathscr {T}}_w^{-1}\) is used). Let us write the LHS of ( A.1 ) in terms of a monomial basis of \(\widetilde{{\textbf{U}}}^\imath \) as

where \(B_J=B_{j_1} B_{j_2} \cdots B_{j_k}\) for some multi-index \(J=(j_1,j_2,\ldots ,j_k)\) with \(j_a\in \mathbb {I}\) and \(a_J \in \textbf{U}^{\imath 0}\) . The lowest weight homogeneous component of \(B_J\) (viewed as an element in \(\widetilde{\textbf{U}} \) ) has weight \(-\textrm{wt}(J)=-\alpha _{j_1} -\ldots -\alpha _{j_k}\) . Denote by \(Q_i:=\{-\textrm{wt}(J)\mid a_J\ne 0\}\) the set of negative weights whose corresponding homogeneous components of the LHS of ( A.4 ) are nonzero. We shall prove that \(Q_i=\emptyset .\)

Recall from ( A.3 ) that \(\textbf{T}_{\omega '_i}^{-1}(B_i) =\widetilde{ \Upsilon }_{\omega '_i}\widetilde{\mathscr {T}}'_{\omega '_i,-1}(B_i)\widetilde{ \Upsilon }_{\omega '_i}^{-1}\) , and by [ DK19 , Lemma  3.6], we have that \(\widetilde{ \Upsilon }_{\omega '_i}\in \bigoplus _{ \alpha \in \mathbb N\Delta (\omega _i')} \widetilde{\textbf{U}} ^+_{\alpha +\tau \alpha }\) . Then any negative weight appearing in the weights of homogeneous components of \(\textbf{T}_{\omega '_i}^{-1}(B_i)\) must have the form \(\alpha _i-\delta +\gamma +\tau \gamma \) , for some \(\gamma \in \mathbb N\Delta (\omega _i')\) . Moreover, since \(\tau i=i\) , the set \(\Delta (\omega _i')\) is fixed by \(\tau \) . Then, by Lemma  3.1 , the multiplicity of \(\alpha _0\) in \(\gamma +\tau \gamma \) for nonzero \(\gamma \in \mathbb N\Delta (\omega _i')\) is at least 2, and recall that the multiplicity of \(\alpha _0\) in \(\delta \) is 1. Hence, by counting the multiplicity of \(\alpha _0\) , the only negative weight appearing in homogeneous components of \(\textbf{T}_{\omega '_i}^{-1}(B_i)\) is \(\alpha _i-\delta \) . It follows by definition that \(Q_i \subseteq \{-2\alpha _i-\delta ,-\delta ,2\alpha _i-\delta \}\) .

A direct computation shows that the homogeneous components of ( A.1 ) of the weights \(-2\alpha _i-\delta , -\delta , 2\alpha _i-\delta \) are the LHS of ( A.5 )–( A.7 ) below, which we claim are all equal to 0:

Indeed, the identity ( A.5 ) follows by [ Be94 , Proposition 3.7]. The identities ( A.6 )–( A.7 ) follow from the identity \(\widetilde{\mathscr {T}}'_{\omega '_i,-1}(F_i) \; E_i = E_i \; \widetilde{\mathscr {T}}'_{\omega '_i,-1}(F_i)\) (see [ Be94 , Lemma  3.4]) and \([E_i,F_i]=\frac{K_i-K_i'}{v-v^{-1}}\) .

This shows that \(Q_i=\emptyset \) and hence the RHS of ( A.4 ) \(=0\) . This proves the desired identity ( A.1 ).

1.2 Proof of Lemma  3.6

It amounts to proving the identities ( 3.5 ), ( 3.6 ) and ( 3.7 ). The identity \([B_i,B_{\tau i}] =\frac{\mathbb K_{\tau i}-\mathbb K_i}{v-v^{-1}}\) in ( 3.7 ) follows by a direct computation.

For convenience we recall the identities ( 3.5 )–( 3.6 ) here as

for \(i\in \mathbb {I}_0\) with \(c_{i,\tau i}=0\) . Let us verify ( A.8 )–( A.9 ); the overall idea is similar to the proof of the identity ( A.1 ).

Recall the braid group symmetry \(\textbf{T}_{i}^{-1}\) (denoted by \(\textbf{T}'_{i,-1}\) in [ WZ23 , Theorem 3.6]) satisfies that

for any \(x\in \widetilde{{\textbf{U}}}^\imath \) . For a reduced expression \(t_{{\varpi }_i'}=\tau _i \textbf{r}_{i_1}\textbf{r}_{i_2} \cdots \textbf{r}_{i_k}\) with \(\tau _i\) a diagram automorphism, we define

By [ WZ23 , Theorem 8.1], \(\widetilde{ \Upsilon }_{{\varpi }'_i}\) is independent of the choice of a reduced expression of \( t_{{\varpi }_i'} \) . Then a repeated application of ( A.10 ) gives us

We prove ( A.8 ). Write the LHS of ( A.8 ) in terms of a monomial basis of \(\widetilde{{\textbf{U}}}^\imath \) as

where \(B_J=B_{j_1} B_{j_2} \cdots B_{j_k}\) for a multi-index \(J=(j_1,j_2,\ldots ,j_k)\) with \(j_a\in \mathbb {I}\) and coefficients \(a_J\) . The lowest weight homogeneous component of \(B_J\) (viewed as an element in \(\widetilde{\textbf{U}} \) ) has weight \(-\textrm{wt}(J)=-\alpha _{j_1} -\ldots -\alpha _{j_k}\) . Denote by \(Q_i:=\{-\textrm{wt}(J)\mid a_J\ne 0\}\) the set of negative weights (in \(-\mathbb N\mathbb {I}\) ) whose corresponding homogeneous components of the LHS of ( A.12 ) are nonzero. We will show that \(Q_i =\emptyset .\)

Note from ( A.11 ) that \(\textbf{T}_{{\varpi }'_i}^{-1}(B_i) =\widetilde{ \Upsilon }_{{\varpi }'_i}\widetilde{\mathscr {T}}'_{{\varpi }'_i,-1}(B_i)\widetilde{ \Upsilon }_{{\varpi }'_i}^{-1}\) , and by [ DK19 , Lemma  3.6], we have \(\widetilde{ \Upsilon }_{{\varpi }'_i}\in \bigoplus _{ {\varvec{\alpha }}\in \mathbb N\Delta ({\varpi }_i')} \widetilde{\textbf{U}} ^+_{2{\varvec{\alpha }}}\) . Then any negative weight component for \(\textbf{T}_{{\varpi }'_i}^{-1}(B_i)\) has weight \(\alpha _i-\delta +2\overline{\gamma }\) , for some \(\overline{\gamma }\in \mathbb N\Delta ({\varpi }_i')\) . Moreover, by Lemma  3.5 , the multiplicity of \(\alpha _0={\varvec{\alpha }}_0\) in \(2\overline{\gamma }\) for \(\overline{\gamma }\in \mathbb N\Delta ({\varpi }_i'){\setminus }\{0\}\) is at least 2, and recall that the multiplicity of \(\alpha _0\) in \(\delta \) is 1. Hence, by counting the multiplicity of \(\alpha _0\) , the only negative weight component for \(\textbf{T}_{{\varpi }'_i}^{-1}(B_i)\) has weight \(\alpha _i-\delta \) . It follows by definition that \(Q_i\subset \{-2\alpha _i-\delta , -\alpha _i-\delta +\alpha _{\tau i}, 2\alpha _{\tau i}-\delta \}\) .

A direct computation shows that the homogeneous components of ( A.8 ) of the weights \(-2\alpha _i-\delta , -\alpha _i-\delta +\alpha _{\tau i}, 2\alpha _{\tau i}-\delta \) are the LHS of ( A.13 )–( A.15 ) below, which we claim are all equal to 0:

Indeed, the identity ( A.13 ) follows by [ Be94 , Proposition 3.7]. The identities ( A.14 )–( A.15 ) can be derived from \([ E_{\tau i},F_i]=0\) and \(\widetilde{T}'_{{\varpi }'_i,-1}(F_i) E_{\tau i}= E_{\tau i} \widetilde{T}'_{{\varpi }'_i,-1}(F_i)\) ; see [ Be94 , Lemma 3.5].

This proves that \(Q_i =\emptyset \) , i.e., the RHS of ( A.12 ) \(=0\) , and hence the identity ( A.8 ).

Just as the identity ( A.8 ) was reduced to the identities ( A.13 )–( A.15 ) above, the identity ( A.9 ) is proved by an entirely similar argument (we skip the details) by reducing to the following identities ( A.16 )–( A.17 ):

The identity ( A.16 ) follows from [ Be94 , Lemma 3.4], while ( A.17 ) follows by a direct computation \([\widetilde{\mathscr {T}}'_{{\varpi }'_i,-1}(F_i),F_{\tau i}] =\widetilde{\mathscr {T}}'_{{\varpi }'_i,-1}\big ([F_i,F_{\tau i}]\big )=0\) , thanks to \(\widetilde{\mathscr {T}}'_{{\varpi }'_i,-1}(F_{\tau i})=F_{\tau i}\) .

This completes the proof of Lemma  3.6 .

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Lu, M., Wang, W. & Zhang, W. Braid Group Action and Quasi-Split Affine \(\imath \) Quantum Groups II: Higher Rank. Commun. Math. Phys. 405 , 142 (2024). https://doi.org/10.1007/s00220-024-05005-7

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DOI : https://doi.org/10.1007/s00220-024-05005-7

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