Perusing Reddit I found someone asking about a hanging chain. The post in question has a semi-quality video of someone whirling a chain from one end in a circle. The rest of the freely swinging chain forms a particular shape as it rotates around some center axis. In short, this happens because of the centrifugal force from the rotation axis against the binding force of the chain links. I want to take some time to really understand this with physics, of course....
5 Centimeters per Second …they say it’s five centimeters per second. The speed of a falling cherry petal. Five centimeters per second. According to the hit 2007 animated short film, 5 Centimeters per Second 1, this is the speed at which cherry petals fall. Of course, I’m skeptical, and as a physicist I want to model the heck out of this. So, in this article I would like to propose a model for a thin, circular flower petal to be the spherical cow of flower petals....
Part 2 of this article Traveling in an Expanding Universe Traveling throughout the Milky Way Galaxy, one can assume a flat universe. So we can assume only special relativity to calculate interstellar travel times for all observers 1. This time I want to expand our interstellar travel calculation to the universal scale. On the universal scale, the universe is not flat, however, but is expanding. We can approximate this expanding universe as a so-called flat Friedmann–Lemaître–Robertson–Walker spacetime....
I was playing on my computer and accidentally tried this expression to see what the computer would output: julia> 9007199254740992.0 + 1.0 == 9007199254740992.0 The REPL output was: julia> 9007199254740992.0 + 1.0 == 9007199254740992.0 true This is obviously incorrect mathematically. However, this arbitrary number is the maximum integer that a 64-bit float can store. In Julia, this number can be found using the maxintfloat function with the Float64 type: julia> maxintfloat(Float64) + 1 == maxintfloat(Float64) true Interestingly enough, adding two “fixes” the comparison:...
Traveling the Stars The speed of light is the ultimate speed limit. This got me thinking about how this fact plays with Einstein’s theory of special relativity. Like if I had a spaceship that was able to provide a constant thrust, how long would it take for me to get to some distant star, say Proxima Centauri. Traveling our Galaxy Let’s set the scene. We have some distance to travel, $L$....
Last time we derived the following Lagragian \begin{equation} L = \sum_{i}^{N}\left( \frac 12 m_i \dot x_i^2 - m_i x_i \right) +F x_1 -\sum_{i=2}^{N}\frac{q}{\gamma - 1} \frac{1}{(x_{i+1} - x_i - \ell_{i})^{ \gamma - 1 }} \end{equation} Where all the the parameters and variables are unitless. Let’s a deeper look at this Lagragian. One thing that stands out is the form of the air compression energy. It only depends on the difference of position variables of the form $x_{i} - x_{i-1}$....
I think it is interesting to sometimes tackle toy examples. For a recent project on a gig economy site, I was presented with a particular physical system which had some nice properties. So here I would like to share with everyone. The system is quite simple, it’s just a vertical cylinder of alternating plugs of water and of air. In the figure above we have a four water plugs as shown as a cross section of a tube....
There have never been so many people in the world. Just a few decades ago, there was science fiction about future worlds, crowded with people. Now, ironically, it’s the opposite. The fertility rate1 is a commonly used term. It’s often said that a fertility rate of 2.1 is needed to sustain a population. I thought today would be a good opportunity to understand the fertility rate and to understand this replacement rate....
The amount of apples can be represented by a number $1,2,3\ldots$. The length and time can also be represented by decimal/real numbers $1.3, \pi, 3,\ldots$. The phase of an electric circuit can be represented by complex numbers! In this sense, physics is useful by abstracting away our world into the world of math. Beyond numbers, another mathematical object is used to represent things like velocity and position. This is the humble vector, an object with both magnitude and direction....
Unit Conversions 1 meter = 100 millimeters = 3.281 feet = 39.37 inches. This is an example of unit conversion. Sometimes, unit conversion is used to convert quantities from an unfamiliar unit to a familiar one. Currently, 1 US Dollar is equivalent to 151 Japanese Yen1 2. At times, the change of unit is for clarity, to express quantities of large or small amounts into comprehensible numbers. For instance, instead of several thousand steps, I find the unit of several miles3 more graspable....