Physics, Math and Science, Explained

Velocity Time Function

Revisiting the Velocity-Time Function

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Kinematics: The Velocity-Time Function Author’s Preface: A Collaborative Approach to Lesson Development The intention behind what I hope will be a series of articles on Kinematics (this one being the first) is to begin an open, collaborative process of lesson development on Physics Forums. In order to expedite this workflow, I am making deliberate use…

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Equations of Motion Revisited

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Introduction In any school Physics course, the Newtonian equations of motion are very much a 'stock' item. Students learn the equations and are given…
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How Bayesian Inference Works in the Context of Science

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Confessions of a moderate Bayesian part 3 Read part 1: How to Get Started with Bayesian Statistics Read part 2: Frequentist Probability vs Bayesian ProbabilityBayesian…
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Confessions of a moderate Bayesian, part 2 Read Part 1: Confessions of a moderate Bayesian, part 1Bayesian statistics by and for non-statisticianshttps://www.cafepress.com/physicsforums.13280237 Background One…
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Abstract The analysis of the two kinds of electric fields, namely the irrotational and non-conservative, is extended to electrodynamics, as exemplified…
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How to Get Started with Bayesian Statistics

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Confessions of a moderate Bayesian, part 1 Bayesian statistics by and for non-statisticianshttps://www.cafepress.com/physicsforums.13265286 Background I…
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Introduction In a homework thread a while back a PF member expressed dismay along the lines of "Oh no, not another boring projectile motion problem."…
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Electric Vector Potential: Detect Non-Conservative Fields

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Main Point The electric vector potential offers a means of determining the non-conservative component of a mixed stationary or quasi-stationary electric…
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I have written many Insights (and coauthored an entire book) explaining how the puzzles, problems, and paradoxes of modern physics can be attributed to…
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Introduction to Pitot-Static Systems in Gliders

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Introduction Like many others, I have been seeking new and fun things to do during a pandemic.   I decided on the new Microsoft Flight Simulator 2020,…
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Why Bother Teaching Mechanical Energy Conservation?

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Note: It is assumed that the reader has read part I and part II of the series. Earlier partsIs Mechanical Energy Conservation Free of Ambiguity? …
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Intro to Centrifugal Force Reversal in Kerr Spacetime

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In this article, we will analyze "centrifugal force reversal" in Kerr spacetime, similar to what was done for Schwarzschild spacetime in a previous Insights…
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Introduction Physics teachers who are either writing physics questions that deal with waves on a string or setting up equipment for a class lab or demo…
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ASOE Physics Past Exams: Yearly Issues & Corrections

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ASOE Physics — Review of Past Exam Issues ref: http://asi.edu.au/programs/past-exams/physics-olympiad-past-exams/Classification of issues: [1*]…
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A Principle Explanation of the “Mysteries” of Modern Physics

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Exploring the Anatomy of Compton Scattering

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Introduction In this article, we take as our starting point the original equations which Compton drew up and solved in his ground-breaking 1925 article:  From…
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The "twin paradox" is often discussed in the introductory treatment of special relativity. Under "twin paradox" we understand the fact that if two twins…
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Android Ringtone Picker using RingtoneManager In article, I will show you how to create a ringtone picker using the RingtoneManager class in Android.…
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5 Experts on How AI Will Reshape STEM: Lab to Classroom

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Answer: AI, and more specifically machine learning, is already reshaping STEM through faster image and data analysis, automated grading and mastery-learning…
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AI in STEM: Physics Forums Advisors Share Their Views

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Physics Forums advisors expect AI to arrive unevenly across STEM: faster in narrow, well-defined tasks like long-haul trucking routes or lab data analysis,…
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Today we get to know a little more about Engineering Mentor jrmichler! Tell us a bit about your education and academic years Two years college (UW-Madison)…
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Are Electromagnetic Waves Always Transverse? Full Explanation

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Electromagnetic (EM) waves are always transverse in the weak sense: the electric field (E) and magnetic field (B) are always perpendicular to the direction…
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How to Solve Second-Order Partial Derivatives

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Introduction A frequent concern among students is how to carry out higher order partial derivatives where a change of variables and the chain rule are…
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Is Pressure A Source Of Gravity?

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In a previous series of articles, I posed the question "Does Gravity Gravitate?" and explained how, depending on how you interpreted the terms "gravity"…
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Massive Meets Massless: Compton Scattering Revisited

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Introduction In a previous article entitled "Alternate Approach to 2D Collisions" we analyzed collisions between a moving and stationary object by defining…
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How should non-scientists evaluate scientists' public claims? In a previous article, I discussed why scientists (among others) are rarely interested…
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The Analytic Continuation of the Lerch and the Zeta Functions

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Introduction In this brief Insight article the analytic continuations of the Lerch Transcendent and Riemann Zeta Functions are achieved via the Euler's…
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Dark Energy Part 3: Fitting the SCP Union 2.1 Supernova Data

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In Part 1 of this 3-part series, I explained kinematics in Einstien-deSitter (EdS) cosmology and in Part 2, I explained kinematics in ##\Lambda##CDM cosmology…
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Dark Energy Part 2: LCDM Cosmology

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This is Part 2 of a 3-part series explaining evidence for so-called “dark energy” leading to a current positive cosmological acceleration. The evidence…
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A Beginner Physics Guide to Baryon Particles

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Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

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Supernova Refsdal: Multiply-Imaged Supernova Guide

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Supernova (SN) Refsdal — Key PointsAstronomers have been trying to understand space for thousands of years. Supernova Refsdal was the first known…
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Cosmic Web Connectivity: How It Shapes Galaxy Evolution

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Researchers simulating the accretion flow around Sagittarius A*, the supermassive black hole at the Milky Way's center, have found that magnetic reconnection…
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The Orin Fractional Calculus

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Introduction This bit is what new thing you can learn reading this:) As for original content, I only have hope that the method of using the sets $$C_N^n:…
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Can We Do Better Than Mechanical Energy Conservation?

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Note: It is assumed that the reader has read part I of the series. Introduction The ambiguity and flaws discussed in part I can be resolved using the…
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Introduction This article follows on from the previous on an alternate approach to solving collision problems. In that article, we determined the equal…
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Is Mechanical Energy Conservation Free of Ambiguity?

Introduction "Close to any question that is in the textbook, there is another question that has never been answered that is interesting." [Stephen Wolfram,…

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Introduction In a previous Insight, A New Interpretation of Dr. Walter Lewin’s Paradox, I introduced the fact that there are two kinds of E fields. …
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Introduction This article is essentially an addition to the previous one on (mainly) inelastic collisions to include the particular case of inelastic…
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Introduction to Evolution Overview The study of evolution has dominated biology for over a century. Explaining why life is the way it is fascinates both…
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Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles…
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Mary Somerville and Caroline Herschel were jointly honored by Google's 2 February 2020 Doodle as the first two women elected honorary members of the Royal…
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Why We Don’t Discuss Perpetual Motion Machines (PMM)

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Authorship Authorship Contributions From Anorlunda Introduction You may want to believe the article you read, or the video you saw, or you may be very…
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Beginner C++ Tutorial — Compiler, Types & I/O Basics

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ContentsGetting a C++ Compiler and Compiling Your First Program Simple Datatypes and Declarations Operators and Expressions Input and Output…
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Video Analysis of Spheres Falling Through Two Liquids

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Introduction Providing accurate fluid-dynamics experiments for undergraduate laboratories is challenging in several ways, including reproducibility, simplicity,…
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Tell One Wood from Another: Basic Wood Anatomy

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Introduction About the author As a long-time woodworker, I enjoy being able to tell one wood from another. In the process of learning how to do that,…
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Explore the Fascinating Sums of Odd Powers of 1/n

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The goal is to get a little bit closer to the values of the zeta function (ζ(s)) and the eta function (η(s)) for some odd values of s. This insight is…
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Learn the Fundamentals of the Diffraction Grating Spectrometer

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Introduction In this article, we will discuss the fundamentals of the diffraction grating spectrometer.  The operation of the instrument is based upon…
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Intro to the Ionization Energy of Atomic Hydrogen

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Introduction In previous articles relating to various transition energies in Hydrogen, Helium, and Deuterium we have employed the following formula for…
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Time to test your science knowledge with a fun 10 question quiz with random questions across all sciences. Difficulty is easy to medium. As always, post…
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SOHCAHTOA: Seemingly Simple, Conceivably Complex

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What is SOHCAHTOA SOHCAHTOA is a mnemonic acronym used in trigonometry to remember the relationships between the sides and angles of right triangles.…
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Android Rooting & Magisk Guide: Systemless Root Tips Overview What you can learn from this article:What is meant by rooting an Android phone …
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Answering Mermin’s Challenge with the Relativity Principle

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Note: This Insight was previously titled, "Answering Mermin's Challenge with Wilczek's Challenge." While that version of this Insight did not involve any…
Conservation of Spin Angular Momentum

Exploring Bell States and Conservation of Spin Angular Momentum

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In a recent thread, I outlined how to compute the correlation function for the Bell basis states\begin{equation}\begin{split}|\psi_-\rangle &=…
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Modern Physics Understood as an Unrecognized Kuhnian Revolution

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People often claim on Physics Forums and in the foundations community proper that quantum mechanics is "incomplete." Indeed, Lee Smolin recently wrote…
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Relativistic Treatment of the DC Conducting Straight Wire

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Introduction The direct-current-conducting infinitely long wire is often discussed in the context of relativistic electrodynamics. It is of course a completely…
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Revisiting The Deuterium Lyman Alpha Line Experiment

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Introduction In this article, we will be revisiting a somewhat understudied (and seemingly unrepeated) experiment to measure the Deuterium Lyman Alpha…
Solar Balmer Lines

Signature of the Sun: Analyzing the Solar Balmer Series Lines

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Introduction We are in many ways a fortunate generation having so many wonderful tools at our disposal on account of the "silicon revolution". The advent…
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Debloating Android Phones: Risks, Myths and Safe Tips

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What is bloatware? Stock firmware and preinstalled apps When you unbox a new phone, it comes with Android pre-installed by the manufacturer. This is…
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Recursion in Programming and When to Use or Not to Use It

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What is recursion? Recursion is quite simple. It's a subroutine calling itself. It's surprising but some problems that look quite hard can be trivial using…
Bohr’s Helium Lines

Understanding Bohr’s Helium Lines

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Introduction In a previous article "Calculating the Balmer Alpha Line" we mentioned how accurate predictions of the spectral lines of singly ionized Helium…
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Maxwell’s Equations in Magnetostatics and Solving with the Curl Operator

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Introduction: Maxwell's equation in differential form ## \nabla \times \vec{B}=\mu_o \vec{J}_{total}+\mu_o \epsilon_o \dot{\vec{E}}  ##  with ## \dot{\vec{E}}=0…
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The Four Laws of Black Hole Thermodynamics Explained

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Black hole thermodynamics consists of four laws that mirror the ordinary laws of thermodynamics: a zeroth law of uniform surface gravity, a first law relating…
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Impedance Explained: Formulas, Equations & AC Circuit Basics

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Impedance is the AC (alternating current) equivalent of resistance. It is a complex number, Z = R + jX, combining resistance R and reactance X, and it…
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How to Ask ‘What If’ Physics Questions: Avoiding Pitfalls

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Overview of "What If" Questions We receive many "what if" questions here on Physics Forums. This article explores three common types and offers suggestions…
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Learn the Basics of Dimensional Analysis

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As a university teacher and as a PF member, I have often noted that students are largely unaware of or not using dimensional analysis to help them in their…
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Mass Inflation in Black Holes: Poisson-Israel Theory Explained

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Mass inflation is the phenomenon in which the internal mass parameter of a rotating or charged black hole grows without bound near the Cauchy horizon,…
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How to Transit a Rotating Tunnel: Physics & Trajectories

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Introduction Preface While browsing through unanswered posts in the Classical Physics Workshop, I came across a gem at the link shown below. For the…
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Calculating the Balmer Alpha Line: Atomic Hydrogen

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Introduction Most readers acquainted with the hydrogen spectrum will be familiar with the set of lines in the visible spectrum representing transitions…
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Maxwell’s Equations in a Static, Spherically Symmetric Spacetime

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In the first article in this series, we looked at the Einstein Field Equations in a static, spherically symmetric spacetime. In this article, we are going…
What is potential energy

Potential Energy Explained: Formulas, Units & Derivations

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Potential energy is the negative of the work done by a conservative force on an object, representing mechanical energy stored due to position within a…
How to Find Potential Functions

How to Find a Potential Function of a Vector Field

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Definition and summary Given a vector field ##\vec F(x,y,z)## that has a potential function, how do you find it? Conditions and equations $$\nabla \phi(x,y,z)…
Moment of Inertia

Moment of Inertia: Formulas, Tensor, and Key Equations

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What Is Moment of Inertia? Moment of inertia is a rigid body property that relates torque to rotational acceleration, playing the same role that mass…
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Understanding Superposition Physically and Mathematically

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What is superposition Superposition is a fundamental concept in physics and mathematics, particularly in the fields of wave theory and quantum mechanics.…
What is Entropy

What Thermodynamics and Entropy Means

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Introduction The student of thermodynamics, as they consider pistons and ideal gasses and such, often begin to grasp the nature of entropy only to find…
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First-Order Linear Equation: Definition & Solutions

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Definition / Summary This article summarizes the first-order (linear) polynomial equation in one variable, its solution, and natural extensions to matrices…
Einstein Field Equation

The Einstein Field Equation in a Static, Spherically Symmetric Spacetime

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This will be the first of several articles which will provide, for reference, useful equations for static, spherically symmetric spacetimes. This is a…
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Significant Figures: Rounding Rules & Examples for Science

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Definition / Summary Significant figures (commonly called "sig figs") are the digits in a number that are considered when rounding a value to reflect…
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How to Write a Math Proof and Their Structure

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Proofs in mathematics are what mathematics is all about. They are subject to entire books, created entire theories like Fermat's last theorem, are hard…
Camera Lens Physics

Evaluate Camera Lens Performance Using an LCD Display

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Introduction I've done plenty of imaging performance testing on a variety of systems, from millimeter wave to UV. Until very recently, such testing required…
Quantum Mechanical Commutator

The Classical Limit of Quantum Mechanical Commutator

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The Classical Limit of Commutator (without fancy mathematics) Quantum mechanics occupies a very unusual place among physical theories: It contains classical…
Minkowski Spacetime

Understanding Precession in Special and General Relativity

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The Absolute Derivative In relativity we typically deal with two types of quantities: fields, which are defined everywhere, and particle properties, which…
What is a fibre bundle

Fibre Bundles Explained: Definition, Examples & Visualization

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A fibre bundle is a mathematical structure consisting of a total space that looks locally like a simple product of two spaces but may have a different…
What are real numbers

Real Numbers Explained: Definition, Axioms & Properties

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Real numbers are the complete set of values on the continuous number line, denoted ℝ, and they include both rational numbers (fractions and repeating…
Star Equations

Equations of State for Photon Gas and Relativistic Electron Gas

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This Insight develops equations of state that are useful in calculations about cosmology and about the insides of stars. The first calculation is for a…
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What is the Double Slit? A 5 Minute Introduction

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Definition/Summary The double-slit is a simple configuration used to demonstrate interference effects in waves.Equations At distances that are…
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What is Integration By Parts? A 5 Minute Introduction

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Definition/Summary In this article, we shall learn a method for integrating the product of two functions. This method is derived from the 'product rule'…
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The 7 Basic Rules of Quantum Mechanics

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For reference purposes and to help focus discussions on Physics Forums in interpretation questions on the real issues, there is a need for fixing the common…
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Clarifying Common Issues with Indistinguishable Particles

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Introduction Commonly there is a lot of imprecision in talking about ''indistinguishable'' (or ''identical'') particles, even in serious work. This Insight…
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A Formal Definition of Large-Scale Isotropy

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This Insight is part of my attempt to develop a formal definition of 'large-scale isotropy', a concept that is fundamental to most cosmology, but that…
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What Is a Parabola? Equations, Focus, and Real Uses

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A parabola is a U-shaped curve where every point is equidistant from a fixed point called the focus and a fixed line called the directrix. Its standard…
Renewable Energy Power Grid

When Renewable Energy Meets Power Grid Operations

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55 Comments
Introduction The electric power industry faces much turmoil in the coming decades.  The business model of the electric utility company (public or private)…
Limit of a Function

What Is a Limit of a Function? Definition, Laws & Examples

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A limit describes the value a function or sequence approaches as its input gets arbitrarily close to a specific point, without requiring the function to…
surface integral

Demystifying Parameterization and Surface Integrals

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Introduction This article will attempt to take the mystery out of setting up surface integrals. It will explain the basic ideas underlying surface integration…