14
votes
Accepted
On constants that maintain proportionality
I don't quite understand the greater meaning behind this. Why does the universe work this way?
Join the club, friend. Physics can only supply the "why" to the point of deriving general ...
- 2,701
14
votes
Relationship between bel and decibel
1 decibel = 0.1 bel.
According to this definition then, 1dB = $\frac{1}{10}$ $log_{10}\frac{P_1}{P_2}$
This is incorrect. Say for example that $P_1=100 P_2$. Then we would have
$$\log_{10}\left(\...
- 67.6k
13
votes
Accepted
Defining the second by an alien civilization
First, neither of your guesses about what is read by a cesium fountain clock are correct. The second guess is much closer though.
The cesium (I'm American, hence American English) fountain clock ...
- 6,331
8
votes
On constants that maintain proportionality
The proportionality constant is woven into the universe. There is no reason it should be any particular number- except that if it were different from what it is, we wouldn't be here to notice it (see ...
- 90.1k
8
votes
Accepted
What does the qualifier NOMINAL exactly refer to?
"Nominal" value in these sorts of engineering contexts means the following. In engineering contexts, we often label things by their values. A great example is a 2x4 piece of lumber. 2 refers ...
- 12.9k
7
votes
On constants that maintain proportionality
People thought about a lot of different ways how this "could" work before they had experimental and observational data that shows "how it actually works", but if we do the ...
- 2,624
6
votes
What does stand behind the formula: "watt = ampere * volt"?
Voltage is not "how many electrons per second you have left after these electrons passed a conductor", because electrons are not "spent" in the process. Rather, voltage is the ...
- 47.2k
6
votes
Accepted
What does stand behind the formula: "watt = ampere * volt"?
Your understanding of voltage is incorrect. The voltage (potential difference) between two points (say, the terminals of a resistor) is the work required (energy in Joules) per coulomb of charge (...
- 69.2k
5
votes
Thermal expansion: why in Celsius and not in Kelvin?
$\Delta T$ is the difference of temperatures - it doesn't matter, whether it is in Celcius or Kelvin, since they differ only by the origin of the scale: $$\Delta T =T_1-T_2=t_1+273.15 - (t_2+273.15)=...
- 57.6k
4
votes
Notation: units with negative exponents
It doesn’t really matter too much, since it’s just a notational convention.
But in some cases you can have fractional or even irrational exponents on the units, in which case the slash notation is ...
- 46.6k
4
votes
Notation: units with negative exponents
RC_23 asked: "I am assuming that some journals, publishers, and authors require or prefer..."
I've seen different notations in the same journal, but you have to keep it consistent within ...
- 11k
4
votes
Accepted
What is stopping optical clocks from redefining the second?
You really shouldn't rush decisions like this. Time keeping is arguably the oldest branch of science, and it usually takes a long time for any changes to the way that people keep time to be decided ...
- 11k
4
votes
Why do we measure plane angle in radians and solid angle in radians and steradians respectively rather than degrees?
For angles, radians are the natural unit, because:
$$ \frac d {d\theta} \cos\theta = -\sin\theta $$
while
$$ \frac d {d\theta}\cos(\frac{\pi}{180^{\circ}}\theta) = -\frac{\pi}{180^{\circ}}\sin(\frac{\...
- 31.6k
4
votes
Unit of $v$ in $v=rω$
The unit radian is dimensionless.
1 radian = 1 m/m = 1.
So the unit of $\omega$ is 1/s.
And the unit of $v=r\omega$ is m/s, as it should be.
- 36.4k
4
votes
Is the unit $m^2$ for area size ambiguous?
You are confusing the unit with the physical quantity.
The unit with which you measure an area should be identified with the unit with which you use to add the squared distance components in ...
- 7,461
3
votes
Frequency of harmonic oscillator potential
Even though the units for $\omega$ are radians/sec, radians have no physical dimension. In both cases the dimensions will be the same. That is, $\text Hz$ and $\text{rad}\ s^{-1}$ have the same ...
- 29k
3
votes
Accepted
Is Coulomb written/found on any object/product as its unit?
The thing that you don't find Coulomb label on any product doesn't means that this product isn't based on charge storage. For example, rechargeable Ni battery with label $2000~\text{mAh}$ stores (when ...
- 11.6k
3
votes
Accepted
Difference between - &
It's a typesetting convention by that author or book publisher. I prefer your way of writing it, but you should not be surprised to see the other way used occasionally.
In the US, the N-m version is ...
- 26.5k
3
votes
Accepted
Relationship between bel and decibel
What you have to remember is what a length $\ell\,m$ means.
The length is $\ell \times (1\rm m)$ where $(1\rm m)$ is a unit of length.
$\rm 1\, m = 1\times (1m)= 100\times (1cm)=100\,\rm cm$
In ...
- 93.8k
3
votes
Relationship between bel and decibel
I wouldn't take an "equation" like
bel = $\log_{10}\frac{P_1}{P_2}$ too seriously. It is confusing at best.
Here is another, arguably neater way to think about things. Suppose $x$ is a ratio ...
- 11.9k
3
votes
Relationship between bel and decibel
A millimeter is 1/1000 of a meter. So if we measure your foot and it is 0.28 meters long, would the length in millimeters be 0.00028 mm or 280 mm?
The formula is telling you how to convert a given ...
- 26.5k
3
votes
Accepted
Does dimensional consistency imply the same units?
Can two units having the same dimensions always be used interchangeably?
This is an interesting question, and a lot hinges on what you mean by “interchangeably”.
If you simply mean the mathematical ...
- 94.6k
2
votes
Accepted
Definition of an electron volt
Hence, by conservation of energy,
electric potential energy = kinetic energy
q x V = K.E
This is not a correct expression for the conservation of energy. The conservation of energy would be $$E_{...
- 94.6k
2
votes
Electric field definition
If we place a small 'test' charge, $q$, in an electric field, we find that the force, $\vec F$, that it experiences due to the field is proportional in magnitude to $q$. Therefore if we divide $\vec F$...
- 34.9k
2
votes
Accepted
Thermal expansion: why in Celsius and not in Kelvin?
No, it is perfectly fine in Kelvins too. You have just mistaken the formula.
Basically, when you see a $\Delta,$ there is very high chance that this is a subtraction of two things.
What the question ...
- 7,461
2
votes
Defining the second by an alien civilization
In the SI system, frequency is measured in Hz. Radiation produced by the transition between the two hyperfine ground states of cesium has a frequency of 9192631770 Hz, by definition. This number was ...
- 76
2
votes
What exactly is kg?
according to its definition, it is the amount of matter contained in an object.
This is incorrect. The actual definition of the kilogram is
The kilogram, symbol $\mathrm{kg}$, is the SI unit of mass....
- 94.6k
2
votes
Is Coulomb written/found on any object/product as its unit?
Coulomb is used wen you have an object wich is charged. du you know what a capacitor is? Or did you do any electro static in class, like a charged sphere? Than you measure the charge in Coulomb. If ...
- 6,023
2
votes
Relationship between bel and decibel
The extract that you have copied is very confusing.
$\log_{10}(P_1/P_2) $ is not the bel, but the relative power expressed in bel(s). If you wanted a definition of the bel (hardly ever sought) it ...
- 34.9k
2
votes
Does dimensional consistency imply the same units?
$s^{-1}$ and $\text{rad}\>s^{-1}$ are not equivalent, note that $1s^{-1}$ implies that one "something" is happening every second, whereas $1 \text{rad}\>s^{-1}$ implies specifically ...
- 6,935
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