The physics of rotation

Welcome to my website featuring the mechanics of rotation.

Animations

Much of the content of this site is illustrated with animations. Rather than conveying the physics with formula's and equations I'm using mathematically correct animations. I do present equations and formula's, but only later on in the articles, after laying down a good understanding.

My purpose is to complement existing sites and existing physics textbooks. What I see in existing material is that the physics of rotation is discussed in an abstract, mathematical way. I want to create a vivid understanding, a 'seat of the pants' understanding.

In writing a site like this I had to decide what level I want to aim for. I assume some familiarity with physics. I would have overburdened the articles if I would have tried to spell everything out for novices.
However, the article Coriolis effect in Meteorology is intended as real introductory material. No math, just visualizations.

In addition to the animations illustrating the articles I have some simulations, which are on separate pages. The simulations were created using EJS, an open source tool for creating models.

Articles

Let me walk you through the various groups of articles that you see in the navigation column on the left.

Coriolis effect related

The article Coriolis effect in Meteorology offers a basic discussion, without using any mathematics.

The sequence of articles starting with Rotational-vibrational coupling is intended to be read in that order. The sequence builds up to the Foucault pendulum article.

The articles about the Eötvös effect and Coriolis flow metering deal with relatively simple manifestations of the Coriolis effect, but since they are not suitable as starting material I have placed them at the rear.

The 'Coriolis in meteorology' article is now also available in French. L'effet Coriolis en météorologie. A visitor, Damien Belliard, who has a meteorology website himself, offered to translate the article, which I gratefully accepted. I can read French fairly well, so I'm happy to publish the translation on my own website.

Rotation

Articles about subjects that are obviously rotation related, such as conservation of angular momentum, but not directly Coriolis effect related

Classical dynamics

Quantity of motion
Momentum and kinetic energy have in common that they express quantity of motion. In this article I discuss relations between symmetry principles and conservation principles, using only the examples of momentum and kinetic energy.

Calculus of variations

Calculus of Variations Using the case of a soap film, stretching between two parallel concentric rings, as motivating example to lay down the foundations of Calculus of Variations, as applied in physics.

Fermat's stationary time. Derivation of Fermat's stationary time from Huygens' principle.

The Catenary. (Not yet in the complete form I want, but all necessary elements are there.) In statics the goal is to identify an equilibrium point. Any system will tend to move towards a point where there is no longer any opportunity to dissipate energy.

Energy-Position equation. In classical mechanics we have F=ma, the Work-Energy theorem, and Hamilton's stationary action. The Work-Energy theorem is the connection between F=ma and Hamilton's action.

Least action visualized. This article has been superseded by the article Energy-Position equation In classical mechanics the work-energy theorem and the principle of least action are mathematically equivalent. The purpose of the article is to demonstrate that with vivid, visual means.

The Sagnac effect

The Sagnac effect falls in the 'physics of rotation' category, but I present it separately. The other articles about the physics of rotation involve only mechanics; the Sagnac effect is a case of wave mechanics; interferometry. Much of the Sagnac effect article deals with a very special case of the Sagnac effect: ring laser interferometry. The rotation effect that is involved in ring laser interferometry is quantummechanical in nature.

Fundamentals

In those articles I discuss very general concepts, dealing with the foundations of theory of motion. I recommend reading the Apparent motion and Inertial coordinate system articles before reading the articles about relativistic physics.

Relativistic physics

Special relativity and General relativity are essays. The information in these essays is very condensed. The purpose is to widen the reader's perspective and provide food for thought. The essays are not introductions, they are intended for readers who have consulted other resources before and will continue to do so. The essays do not contain any mathematics in the form of equations; all the abstract concepts are conveyed with animations and diagrams.

Relativistic physics has been around for a hundred years now, but the understanding of relativistic physics is still evolving. The essays here are inspired by developments of the past couple of decades.

EJS

Visit the EJS website to learn about EJS.
The Open Source physics section of the comPADRE website is, among other things, a repository for simulations with their documentation.

Simulations created with EJS.

Inertial oscillation
The inertial oscillation model represents the essence of the rotation of Earth effect that is taken into account in Meteorology and Oceanography.
- Inertial oscillation math. Discussion of the simulation's mathematical setup.

Great circles.
This is an interactive animation. The model represents the essence of the rotation of Earth effect that is is relevant for ballistics.

Ballistics and orbits
The trajectory of a ballistic missile is a keplerian orbit. In this simulation projectiles can be fired straight up or at any other angle, thus showing the rotation-of-Earth effects that are at play.

Circumnavigating pendulum.
A vibrating object experiences an elastic force; a restoring force that acts towards the point of attraction. What if that point of attraction is in uniform circular motion? This simulation explores that setup.

Foucault pendulum
While there are many Foucault pendulum animations on the web, this is a simulation. The emphasis of the Foucault pendulum simulation is on why the pendulum moves in the way that it does: at the poles, at midlatitudes and at the equator.
- Foucault pendulum math. Discussion of the simulation's mathematical setup.

Foucault Rod
This is a general simulation, that in effect combines features of the circumnavigating pendulum simulation and the Foucault pendulum simulation. In this simulation the pendulum is a rod with a bob at the end. The simulation can be run with any combination of orientation of the rod and distance of the bob to the central axis of rotation.

Angular acceleration of a contracting system
A model with a pulley system illustrates what happens when a rotating system contracts. The centripetal force is doing work, causing angular acceleration.

Spacestation vertical throw
Imagine you are onboard a rotating spacestation. If you throw an object, and you want it to land right at your feet again, in what direction do you need to aim?

Articles

As you will have noticed, I'm referring to the material on my site as 'articles'. The layout of this site is inspired by Wikipedia. In particular I have copied the way that images are displayed on Wikipedia.

I like to think of my material as as entries in an encyclopedia. It's presentation of background material rather than teaching a course.

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.