Expert Math and Science Articles

Quaternions in Projectile Motion

Quaternions in Projectile Motion

/2 Comments/in /by

Introduction In a previous Physics Forums article entitled “How to Master Projectile Motion Without Quadratics”, PF user @kuruman brought to our attention the vector equation  ##\frac{|V_0 \times V_f|}{g} = R## and lamented the fact that: “Equally unused, untaught and apparently not even assigned as a “show that” exercise is Equation (4) that identifies the range as the…

Trending Articles

Recent Entries

safety

When Science is Not Enough: Legal and Health Implications of Questions

7 Comments
/
There are often questions on Physics Forums related to building machines or structures that are left unanswered because of this guideline (found in the…
LCEVC 8k tv

The LCEVC Coding Standard and 8K Television

4 Comments
/
Introduction First, for background, here is an overview of the most common video compression standard in use today, H264: https://www.maketecheasier.com/how-video-compression-works/H265…
solving projectile motion

How to Solve Projectile Motion Problems in One or Two Lines

1 Comment
/
Introduction We show how one can solve most, if not all, introductory-level projectile motion problems in one or maybe two lines. To this end, we forgo…
blackboard

10 Math Things We All Learnt Wrong At School

10 Comments
/
The title is admittedly clickbait. Or a joke. Or a provocation. It depends on with whom you speak, or who reads it with which expectation. Well, I cannot…
Fourier Series Riemann Zeta Function

Computing the Riemann Zeta Function Using Fourier Series

5 Comments
/
Euler's amazing identity The mathematician Leonard Euler developed some surprising mathematical formulas involving the number ##\pi##. The most famous…
tolman law beginner

Tolman Law in a Nutshell

46 Comments
/
The Tolman law describes how the temperature in a fixed gravitational field depends on the position (see https://arxiv.org/abs/1803.04106 for a pedagogic…
physics cannonball projectile

Maximizing Horizontal Range of a Projectile

7 Comments
/
Introduction A recent homework problem that appeared in the forums was concerned with maximizing the horizontal range of a projectile subject to the launch…
electromagnetic computations duality

A Numerical Electromagnetic Solver Using Duality

0 Comments
/
In the previous insights article (How to Use Duality in Computational Electromagnetic Problems), I covered some uniqueness theorems for the Riemann-Silberstein…
Electric Field Seen by an Observer

The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors

0 Comments
/
This Insight was inspired by the discussion in "electric field seen by an observer in motion", which tries to understand the relation between two expressions:…
valentines reflections graphs

Valentine’s Reflections: Mathematical Matters of the Heart

4 Comments
/
Introduction Being a somewhat geeky Maths 'nerd', I spent days leading up to Valentine's day trying to find a Maths function appropriate to the day. In…
Bayesian statistics part 4

Posterior Predictive Distributions in Bayesian Statistics

7 Comments
/
Confessions of a moderate Bayesian, part 4 Bayesian statistics by and for non-statisticiansRead part 1: How to Get Started with Bayesian StatisticsRead…
electromagnetic computations

How to Use Duality in Computational Electromagnetic Problems

1 Comment
/
Some weeks ago I happened across a post that caught my eye. Dale asked a question about the number of photons in an electromagnetic field. His question…
equations of motion

Equations of Motion Revisited

1 Comment
/
Introduction In any school Physics course, the Newtonian equations of motion are very much a 'stock' item. Students learn the equations and are given…
bayesian inference

How Bayesian Inference Works in the Context of Science

12 Comments
/
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…
bayesian statistics part 2

Exploring Frequentist Probability vs Bayesian Probability

38 Comments
/
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…
Split Electric Fields

Split Electric Fields in Electrodynamics: Capacitor and Antenna

0 Comments
/
Abstract: The analysis of the two kinds of electric fields, namely the irrotational and non-conservative, is extended to electrodynamics, as exemplified…
bayesian statistics

How to Get Started with Bayesian Statistics

13 Comments
/
Confessions of a moderate Bayesian, part 1 Bayesian statistics by and for non-statisticianshttps://www.cafepress.com/physicsforums.13265286 Background I…
projectile motion

How to Master Projectile Motion Without Quadratics

6 Comments
/
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."…
electric potential

Introduction to Electric Vector Potential and Its Applications

16 Comments
/
Main Point: The electric vector potential offers a  means of determining the non-conservative component of mixed stationary or quasi-stationary electric…
Learn the Math

I Know the Math Says so, but Is It Really True?

66 Comments
/
I'm sure anyone who has hung out long enough here on Physics Forums has encountered threads that go something like this (I'll use an example based on threads…
block universe time illusion

Does the Block Universe of Physics Mean Time is an Illusion?

29 Comments
/
I have written many Insights (and coauthored an entire book) explaining how the puzzles, problems, and paradoxes of modern physics can be attributed to…
flight simulator

Introduction to Pitot-Static Systems in Gliders

1 Comment
/
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, but the Condor…
mechanical conservation of energy

Why Bother Teaching Mechanical Energy Conservation?

7 Comments
/
Note: It is assumed that the reader has read part I and part II of the series.Is Mechanical Energy Conservation Free of Ambiguity? Can We Do Better…
kerr spacetime centrifugal force

Intro to Centrifugal Force Reversal in Kerr Spacetime

0 Comments
/
In this article, we will analyze "centrifugal force reversal" in Kerr spacetime, similar to what was done for Schwarzschild spacetime in a previous Insights…
strings waves

Intro to Physically Reasonable Waves on a String

4 Comments
/
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…
Physics Olympiad Corrections

Corrections to the Australian Physics Olympiad Questions and Solutions

3 Comments
/
ref: asi.edu.au/programs/past-exams/physics-olympiad-past-exams/ Classification of issues: [1*] Quibble regarding the solution. [2*] Clearer problem…
physics mysteries

A Principle Explanation of the “Mysteries” of Modern Physics

93 Comments
/
All undergraduate physics majors are shown how the counterintuitive aspects ("mysteries") of time dilation and length contraction in special relativity…
Compton Scattering

Exploring the Anatomy of Compton Scattering

1 Comment
/
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…
Twins Paradox

Learning the Twin Paradox for Freely-falling Observers

1 Comment
/
The "twin paradox" is often discussed in the introductory treatment of special relativity. Under "twin paradox" we understand the fact that if two twins…
android ringtone

Create an Android Ringtone Picker Using the Ringtonemanager Class

3 Comments
/
In this article, I will show you how to create a ringtone picker using the RingtoneManager class in Android. You will be able to get the list of tones,…
artificial intelligence

The Rise of AI in Classrooms, Labs and Industry – Part 3

0 Comments
/
We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many…
artificial intelligence

The Rise of AI in STEM – Part 2

0 Comments
/
We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many…
artificial intelligence

The Rise of Artificial intelligence in STEM Labs, Classrooms, and Industry

1 Comment
/
We asked our PF Advisors "How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?". We got so many great…
jrmichler engineer interview

Interview with Engineer jrmichler

0 Comments
/
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)…
electromagentic waves traverse

Are Electromagnetic Waves Always Transverse?

5 Comments
/
In this insight, we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko's…
calculus

How to Solve Second-Order Partial Derivatives

1 Comment
/
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…
pressure is a source of gravity

Is Pressure A Source Of Gravity?

11 Comments
/
In a previous series of articles, I posed the question "Does Gravity Gravitate?" and explained how, depending on how you interpreted the terms "gravity"…
Compton Scattering

Massive Meets Massless: Compton Scattering Revisited

0 Comments
/
Introduction In a previous article entitled "Alternate Approach to 2D Collisions" we analyzed collisions between a moving and stationary object by defining…
Science Authority

Is Science an Authority? How to View Announcement from Scientists

66 Comments
/
In a previous article, I discussed why scientists (among others) are almost never interested in considering a new theory proposed by a non-scientist: because…
lerch and zeta functions

The Analytic Continuation of the Lerch and the Zeta Functions

0 Comments
/
Introduction In this brief Insight article the analytic continuations of the Lerch Transcendent and Riemann Zeta Functions are achieved via the Euler's…
dark energy supernova

Dark Energy Part 3: Fitting the SCP Union 2.1 Supernova Data

0 Comments
/
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…
dark energy cosmology lcdm

Dark Energy Part 2: LCDM Cosmology

0 Comments
/
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…
beginner guide to baryons

A Beginner Physics Guide to Baryon Particles

9 Comments
/
Introduction At the beginning of the 20th century, it was thought that all matter consisted of only three particles: the electron, the neutron, and the…
symmetric spacetime

Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

0 Comments
/
In the first two articles in this series, we looked at the Einstein Field Equation and Maxwell's Equations in a static, spherically symmetric spacetime.…
supernova refsdal

The Reappearance of Supernova (SN) Refsdal

0 Comments
/
Space is always changing. Over thousands of years, astronomers have attempted to understand the workings. Trying to explain astronomical events offers…
Dark Energy Cosmology Part 1

Dark Energy Part 1: Einstein-deSitter Cosmology

6 Comments
/
In this 3-part series, I want to motivate the (re)introduction of the cosmological constant ##\Lambda## into Einstein's equations of general relativity…
Evidence for Big Bang

Universe FAQ: Is there Evidence for the Big Bang?

0 Comments
/
Evidence for the big bang can be provided from observational astronomy using Hubble’s law (redshift of galaxies) also known as the ‘Doppler effect’…
Cosmic Web Connections

The Evolution of the Universe, Cosmic Web and Connections

1 Comment
/
The universe was not perfectly uniform when it started, some areas had a higher density than others. During the evolution of the universe, these areas…
Gaia search for black holes

Gaia and the Race to Detect More Gravitational Waves

1 Comment
/
Gravitational waves (GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most…

3 Possible Models For Why Uranus Spins on Its Side

4 Comments
/
Uranus spins on its side. Uranus has an obliquity (tilt) of 98º, making its axis of rotation closer to the ecliptic plane than any other planet. It is…

Black Holes Are Not Empty Voids. A Black Hole at the Heart!

9 Comments
/
Black Holes (BH’s) are curious because of their mysterious nature and unknown properties. BH’s are not empty voids. They are astronomical objects…