## The Slinky Drop Experiment Analysed

The slinky drop is a rather simple experiment. In its most basic form, it requires only a popular toy for children, a stable hand, and a keen eye. For a better view, using a modern smartphone to capture a video of the experiment also helps to capture the falling slinky. Apart from the commonly quoted…

## A Physics Misconception with Gauss’ Law

Introduction It is relatively common to see the following type of argument: The surface area is ##A## and the enclosed charge is ##Q##. The electric field strength on the surface is therefore ##E = Q/\varepsilon_0 A##. The problem is that this statement is only true in very special cases. In this Insight, we discuss the…

## How Can We Jump When the Ground Does No Work?

It is relatively common on Physics Forums to see arguments that are effectively similar to the following: When we jump off the ground, the ground does not move. Because of this, the force from the ground on us does zero total work. Since the force does no work, we cannot gain any kinetic energy. We…

## Symmetry Arguments and the Infinite Wire with a Current

Many people reading this will be familiar with symmetry arguments related to the use of Gauss law. Finding the electric field around a spherically symmetric charge distribution or around an infinite wire carrying a charge per unit length are standard examples. This Insight explores similar arguments for the magnetic field around an infinite wire carrying…

## Learn the Basics of Dimensional Analysis

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 pursuit of knowledge or to check their results. Several recent threads on PF have also highlighted this issue. The intent of this Insight is therefore to…

## The 10 Commandments of Index Expressions and Tensor Calculus

Having more than 10 years of experience in teaching vector and tensor calculus and special and general relativity, I have noted that many people have the same problems when trying to manipulate index expressions. The problem often lies in being familiar with the very basic ideas, such as repeated indices implying a sum (the summation…

## Explore Coordinate Dependent Statements in an Expanding Universe

In this Insight, we will discuss the general Robertson-Walker (RW) universe, in which a set of co-moving observers with proper time ##t## observe the universe to be homogeneous and isotropic. In such a universe, the line element takes the form $$ds^2 = dt^2 – a(t)^2 [dr^2 + f(r)^2 d\Omega^2] \equiv dt^2 – a(t)^2 dS^2,$$ where…

## The Birth of a Physics Textbook: An Author’s Journey

It is said that you should accomplish three things in life: Plant a tree. Have a child. Write a book. Out of the three, I have completed at least one. At the time of writing this Insight, my textbook “Mathematical Methods for Physics and Engineering” just hit the virtual online shelves. This Insight will…

## Learn About Knut Lundmark and the Prehistory of Dark Matter

Look in your standard cosmology textbook (in my case, the closest one at hand is Barbara Ryden’s Introduction to Cosmology) and go to the section that describes the experimental discovery of dark matter. Two of the things you will likely find in there are the following pieces of information: The virial theorem was applied to…

## A Geometrical View of Time Dilation and the Twin Paradox

Based on the number of questions we receive on the topic at Physics Forums, there is a lot of confusion in the general public about how time dilation works and the resolution of the twin paradox. More often than not, the confusion is based upon misunderstandings about how time dilation works and an unawareness of…

## What is relativistic mass and why it is not used much?

It happens that the term relativistic mass is used, in particular in the introductory text on special relativity. It should be noted that whether or not to use relativistic mass to a large extent is a matter of convention, convenience, and semantics as long as it is used properly and does not have any impact…

## Plus/minus What? How to Interpret Error Bars

People sometimes find themselves staring at a number with a ± in it when a new physics result is presented. But what does it mean? This Insight aims to give a fast overview of how physicists (and other scientists) tend to present their results in terms of statistics and measurement errors. If we are faced…