Measuring the Atmosphere from Inside the Moon's Shadow
A total solar eclipse and its lunar shadow over Valencia de Don Juan turn a panorama into an experiment on the height and cooling of the atmosphere.
Topic
Physics
Mechanics, thermodynamics, and useful physical reasoning.
Estimating the Dipole Radiation Power using Dimensional Analysis
An electric dipole is characterized by the dipole moment $d$ which depends on both the charge $e$ and a the separation $s$ (but not independently on each). Estimating the power radiated by an oscillating electric dipole is an excellent example for the usage of dimensional…
The Standard Model Lagrangian
If you're wondering about the equation in the banner, it is the Lagrangian of the standard model . It is the most succinct way of writing the laws governing the strong, electromagnetic and weak forces and their interaction with the known particles. The origin of this hand written…
Predicting a supernova precursor (on SN2010mc)
A very interesting paper recently appeared in nature . It describes the detection of a precursor eruption of a supernova progenitor more than a month before the supernova explosion itself. It is particularly interesting because this detection was not serendipitous—it was based on…
Dust Dendrites
My wife and I had our kitchen renovated aaa. Since this involved breaking a few walls (and cutting out a new window), we knew it would raise a lot of dust. Mind you, here in the middle east houses are built from concrete and concrete blocks, not wood. To minimize the dust…
Characteristics of an LC circuit using Equipartition
An LC circuit is one which has a capacitor and an inductor connected to each other. It exhibits oscillations just like a mass on a spring (a harmonic oscillator). In fact, the analogy is quite accurate with the capacitor playing the role of the spring and the inductor playing the…
Estimating the Size of the Hydrogen Atom (i.e., Bohr's Radius) using Equipartition
Peering into the hydrogen atom . The standard way to obtain the size of the hydrogen atom, also known as Bohr's radius, is to solve Schrödinger equation for the hydrogen atom. This is a somewhat detailed calculation requiring the usage of generalized Laguerre polynomials and…
Why don't I believe the that neutrinos travel faster than the speed of light?
Three weeks ago I visited the underground laboratory of Gran Sasso near l'Aquila. Little did I know that it would make headline news so soon, for "discovering" particles moving faster than the speed of light. Since a few people asked me what did I think of it, I decided to write…
From Masada to the Messinian Salinity Crisis
Masada, the Dead Sea, the Messinian Salinity Crisis and Augustus Ceasar, all in one post.
A visit to Stromboli
Last May I had a conference in the island of Vulcano. During the conference I had a half day excursion to the Island of Stromboli, where I climbed the mountain and got to see one of the most impressive geological phenomena one can see... Here are my impressions, photos and even a…
Bush in a quantum entangled state
On my personal views of President Bush's visit to my humble town of Jerusalem. A few thoughts about quantum mechanics and the speed of sound.
The Dot Product
The dot product.
Scalar and Vector Algebra
Scalars : Scalars are mathematical entities which include only a magnitude (and no direction). Physical examples include mass and energy. Vectors : Vectors are mathematical entities which include both a magnitude and a direction . Note that the location of the vector (for…
Corpuscular Rays in St. Peter's Basilica (the Vatican)
A few days ago, I stayed in the Vatican (more about this one day symposium in another post). During the stay, I naturally visited St. Peter's Basilica. Near Bernini's Altar, I saw corpuscular rays. It may seem like some godly thing (quite appropriate for the location), but from a…
Stokes Drag (free fall + linear air drag force)
Let us study a somewhat more complex case of motion in a gravitational field. Instead of just the force of gravity, let us add a drag force which is proportional to the velocity, that is: $$ { F} = - { v}. $$ In other words, at every instant, the drag force is proportional to the…
Newton's laws
Newton's laws and other laws of nature cannot be "derived" or "proved" like proofs in Math. Instead, physical laws are conjectured and then studied through experiments. These laws can be verified under different limits, in which case the conjected laws become accepted theory, or…
Transformation of Forces in Relativity
We have previously seen that the velocity does not transform from one reference frame to another using the standard Lorent transformation to 4-vectors, simply because the velocity is not a 4-vector. Similarly, the force is not one either (nor is it part of one, such as the…
Forces in Relativity
Until now, we have avoided using forces in Relativity. We did so for a good reason. The definition of force even in classical mechanics is somewhat problematic, let alone in relativity. Nonetheless, let us try and see whether we can generalize classical relations to get a…
Chapter 13: A Few Extras
Chapter 13: A Few Extras
Chapter 12: Relativistic Dynamics
Chapter 12: Relativistic Dynamics
Chapter 11: Relativistic Kinematics
Chapter 11: Relativistic Kinematics
Chapter 10: Rigid Body
Chapter 10: Rigid Body
Chapter 9: Non-Inertial Frames
Chapter 9: Non-Inertial Frames
Chapter 8: Central Force
Chapter 8: Central Force
Chapter 7: Harmonic Motion
Chapter 7: Harmonic Motion
Chapter 6: Center of Mass & Angular Momentum
Chapter 6: Center of Mass & Angular Momentum
Chapter 5: Energy
Chapter 5: Energy
Chapter 4: Momentum
Chapter 4: Momentum
Chapter 3: Newton's laws, forces, equations of motion
Chapter 3: Newton's laws, forces, equations of motion
Units and Dimensions
Units are part of physical quantities. This implies that a physical variable will have a value and may include a dimension such as length, time, mass or combinations of them. For example, x = 5 meters , t = 3 seconds , v = 5/3 meter per second = 5/3 m/sec , m = 10 kg or E = 2 J…
A Nice Black Hole Merger Simulation
I recently stumbled upon a nice black hole merger simulation . Since it is not in my habit of just regurgitating stuff I see on the internet, here is my added value. How can one estimate the quadrupole gravitational radiation of a binary? How close does the binary have to be for…
A short history of Mechanics
The first to seriously ponder about the nature of nature where the ancient Greeks. However, following the Aristotlian views, logic was more important than experiment. Since it is logical that heavier bodies fall faster to the ground, it necessarily is the case. For example, an…
Chapter 2: Mathematical Background
Some necessary mathematical background
A few words on the course
If you are reading these lines, you either accidentally stumbled upon or deliberately looked for Mechanics and Relativity course notes. These notes are used in the first year physics major's classical mechanics course. They were prepared over the course of 3 semesters whilst I…
Chapter 1: Introduction
Some Introduction
Classical Mechanics and Relativity
Online notes for a physics major's classical mechanics and relativity course. The course notes are still in the making, and will be added during January / February 2008
Parhelic Circles, Ice Haloes and Sun dogs over Jerusalem
A few weeks ago, a few students saw a nice phenomenon in the sky. Knowing I liked this kind of stuff (and that I may be able to explain it), they called me out of the office to look at the sky. Above us was a nice and almost complete parhelic circle . Unlike the usual 22° halo…
Standing on ice - When is it possible?
Ever wondered whether it was sufficiently cold for sufficiently long to allow you to stand on ice, without falling in? I once did. Here is an estimate for the duration required to reach a given thickness. Actually, it is a lower limit, since we assume a few simplifying…
Estimating Stellar Parameters from Energy Equipartition
Many physical systems have a tendency to equilibrate the energy between different subcomponents. Sometimes it is exact, and sometimes not. For example, in an acoustic wave, the wave's energy is on average half kinetic (motion of the gas) and half internal (pressure). In the…
Have you heard of the silent Earthquake?
Did you know that there are huge earthquakes which aren't felt? Did you know that similar waves appear everyday when two objects with dry friction between them start to move?
Exhale Condensation Calculator
Determine whether mixed exhaled and outside air condenses and estimate the mixing range and cloud-water content.
Snow probability calculator
Estimate the melting temperature and probability that falling precipitation reaches the ground as snow.
Snow at above freezing temperatures
Did you ever wonder how can it snow at above freezing temperatures? Well, the naive explanation is that it simple takes time for the snowflakes to melt once they penertrate above freezing air, as they descent downwards to the ground. As it turns out, this is the reaons why hail…
Water Rocket Simulator
Numerically simulate a homemade water rocket and graph its velocity and height over time.
The Transit of Venus
Twice every 117 years or so, Venus transits the disk of the sun. Here is some info on the events (and a photograph I took of it).
Row Row Row your Boat - At which maximum speed?
The maximum speed of a rower boat is a classic example of the beauty of dimensional analysis. It was originally derived by McMahon (1971). Here it is brought again for the convenience of the Internet audience, together with updated rowing record data. First, some assumptions…
The Milky Way Galaxy's Spiral Arms and Ice-Age Epochs and the Cosmic Ray Connection
On long time scales, it appears that our journey through the Milky Way is responsible for large climate variations. Each time we pass through spiral arms of the galaxy, we witness a higher flux of cosmic rays, which in turn reduce the global temperature. Read more about the…
Frost Dendrites
Under which conditions can you get frost dendrites on your window?
The Foucault Pendulum
The Foucault Pendulum was conceived by Léon Foucault in the middle of the 19th century, with the goal of proving Earth's rotation through the effect of the Coriolis Force. In essence, the Foucault Pendulum is a Pendulum with a long enough damping rate such that the precession of its plane of oscillations can be observed after typically an hour or more. A whole revolution of the plane of oscillation takes anywhere between a day if it is at the pole, or longer at lower latitudes. Here is a relatively simple derivation of the precession.
Condensation of your exhaled breath
Ever wondered why and when does your exhaled breath condense?
Dimensionless Numbers
Dimensionless numbers are VERY important in the understanding of physical problems and their solution. In particular, The value of the dimensionless numbers often determine the behavior of the solution. For example, a flow problem with a low Reynolds Number will be laminar, while…
More interesting physics
PhysicsBits articles and the general-physics blog archive.
Weather related physics
Weather and climate physics articles, explanations, and calculators.