Jerks are even in physics

Hi,
the title is a pun. There are probably jerks yes, but what I want to talk about is physical unit[1] called jerk, it is named like this because jerk not only means, idiot or stupid, but also to move suddenly, because of surprise.


It will be nice, if we first recall that derivation describes the rate of change of something. For example, speed is the first derivative of position because speed describes the rate of change of position, the higher the speed the more position changes!

{\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {x}}}{\Delta t}}={\frac {d{\boldsymbol {x}}}{d{\mathit {t}}}}.

1st derivation of position “compared” to time

In the picture above you can see how speed is defined compared to position (x) and time (t). It is its derivative as I said before. Now of course you can define something, that describes how velocity changes over time. That is called acceleration.

\mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}

Again, “d” simply means derivation and when it is “squared” it means that you need to derive it twice. Acceleration describes, how velocity changes over time.

This is all you might need for daily life. Of course though, scientists defined next derivations, the change of acceleration in time is called jerk. The change of jerk is called jounce the change of jounce is crackle, next follows pop and then possibly lock, drop, shot and put. The SI units of all of these time, position related things are similar. With each derivation you add one to exponent of time.

v=m/s¹
a=m/s²
j=m/s³

and so on..

Just to remind you, if you have lets say “pop”, which is 6th derivation, of 10 m/s^6 you will have a tremendous speed extremely fast. From this next equation it should be pretty clear:

{\displaystyle {\vec {r}}={\vec {r}}_{0}+{\vec {v}}_{0}\,t+{\frac {1}{2}}{\vec {a}}_{0}\,t^{2}+{\frac {1}{6}}{\vec {\jmath }}_{0}\,t^{3}+{\frac {1}{24}}{\vec {s}}_{0}\,t^{4}+{\frac {1}{120}}{\vec {c}}_{0}\,t^{5}+{\frac {1}{720}}{\vec {p}}\,t^{6}}

The power of the higher derivations is that the exponent does extreme changes in a moment. r is the position, v speed, a acceleration… p is pop and t is time.

This is probably not used much, if at all, even in engineering.. but hey, fun!

Dragallur

[1]It is not a unit. It is physical quantity or something like that. I do not really know how it is called in english.

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Cycling faster than light

Hi,
so while I was learning some optics, I bumped into this page that talked about refractive index which I was just studying. I wondered what is the highest refractive index ever found and there it was, not in number though I think we can calculate it.


Refractive index

Since you probably have not read my post about refractive index or you have not heard about it, it is dimensionless value that shows how much is light (electromagnetic radiation) slow in the medium where it travels and also how much it will change its direction when traveling through one medium into the other. You can calculate the index like this:

n=c/v

Where n is the refractive index, c is speed of light in vacuum and v is the velocity in the medium you are talking about. From this, it is easy to see that vacuum and only vacuum has the refractive index exactly 1 because there is nothing that blocks its way and you just divide speed of light in vacuum by speed of light in vacuum.


So as the index of refraction increases the only thing that can change is velocity in the medium and it is decreasing.

I found that scientists were able to create stuff in which the light was traveling in “only” 17 meters per second! This is 61.2 kilometers per hour. From steep hill or if you are really good cyclist you can be faster than that, though I think it is bit more easier and safer to do it in car.

So what is the refractive index of this miraclous stuff? Roughly 17,647,059. While normally n lies somewhere between 1 to 3.

What is this thing made of? 

… gas of sodium atoms – a high-tech version of the insides of the bulbs of street lamps – cooled to within a fraction of a degree above absolute zero … the effect of cooling reduces thermal effects, and this in itself contributes to the retardation of light.

There is also special state of matter created that packs those atoms closer together.

Dragallur