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212 votes
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Is $\pi^2 \approx g$ a coincidence?

The differential equation for a pendulum is $$\ddot{\phi}(t) = -\frac{g}{l}\cdot\sin{\phi(t)}$$ If you solve this, you will get $$\omega = \sqrt{\frac{g}{l}}$$ or $$T_{1/2}=\pi\sqrt{\frac{l}{g}}$$ $...
Anedar's user avatar
  • 1,981
156 votes
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Why are "degrees" and "bytes" not considered base units?

The radian (not the degree) is the SI unit of angle, and it's defined in terms of lengths: it is that angle for which the length of a circular arc subtending that angle is equal to the radius of the ...
Michael Seifert's user avatar
113 votes
Accepted

Is Nm the same unit of torque as mN?

Just like $2\times3=3\times2$, There is no difference between newton-meters and meter-newtons. They're two different ways of saying the same thing. Probably your book is trying to avoid confusion when ...
The Photon's user avatar
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101 votes

Has anyone charged an object with 1 coulomb? Why was such a ridiculously large charge chosen as the unit of charge?

Actually the ampere (SI unit for electric current) was defined first (in 1881, see Wikipedia: Ampere - History). They chose this size for $1$ ampere, probably because at this time such a current could ...
Thomas Fritsch's user avatar
57 votes

Is $\pi^2 \approx g$ a coincidence?

It's annoyingly unclear how far it's a coincidence, but at any rate it isn't completely a coincidence. As you can see in e.g. the Wikipedia article about the metre, a unit almost equal to the metre ...
Gareth McCaughan's user avatar
53 votes

Has anyone charged an object with 1 coulomb? Why was such a ridiculously large charge chosen as the unit of charge?

Has anyone charged an object with 1 coulomb? Not a problem nowadays with supercapacitors. Why was such a ridiculously large charge chosen as the unit of charge? Once the second and the ampere (both ...
Farcher's user avatar
  • 97.9k
53 votes

What is a joule? I find the definition confusing

Pushing the ball bearing with 1 N for one meter and pushing a bowling ball with 1 N for 1 meter do exactly the same amount of work: 1 joule. As you say: it will take a much longer time for the ...
mike stone's user avatar
  • 54.5k
51 votes

Will the volt, ampere, ohm or other electrical units change on May 20th, 2019?

Late last century electrical standards based on Josephson junctions became common. A Josephson junction together with an atomic clock can give an exquisitely precise voltage standard in terms of the ...
Dale's user avatar
  • 103k
51 votes

Why is the length of the Kelvin unit of temperature equal to that of the Celsius unit?

Kelvin history The kelvin unit was designed so that a change of $1\ \text{K}$ corresponds to a change of $1\ ^\circ\text{C}$. This makes sense because people were working in Celsius at the time. ...
Jagerber48's user avatar
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44 votes
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Is the fact that 100 kPa equals about 1 atmosphere accidental?

This is a coincidence. There's nothing about the atmosphere that would make it have a nice relationship with the Earth's rotation or diameter, or the fact that water is plentiful on the surface. On ...
Emilio Pisanty's user avatar
43 votes
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Why do we use the electron volt?

The electron-volt is a convenient unit of energy when considering electrons moving between points at different potentials. The convenience came from having numerical values which are around or ...
Farcher's user avatar
  • 97.9k
43 votes
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Is the definition of a meter tautological?

Theoretically, we have not defined the speed of light in terms of the metre. We have defined it as a specific distance (that light can cover in one second). Now take that distance and divide it with $...
Steeven's user avatar
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38 votes
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Has anyone charged an object with 1 coulomb? Why was such a ridiculously large charge chosen as the unit of charge?

The underlying reason that 1 coulomb seems like a large amount of charge is that most charged particles in ordinary settings are nonrelativistic -- moving at speeds $v$ much less than the speed of ...
nanoman's user avatar
  • 3,870
36 votes

Is there any truth to interpreting definition of a second as corresponding to oscillations?

The definition for the cesium clock is: 9192631770 cycles per second is frequency of the radio waves which cause maximum resonance, a physically measurable condition, in the cesium atoms. This ...
Peter Diehr's user avatar
  • 7,205
36 votes
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The definition of 1 kelvin

To answer this question it may help to take an example from a more familiar area of physics, and then discuss temperature. For a long time the kilogram (the SI unit of mass) was defined as the mass of ...
Andrew Steane's user avatar
36 votes

How long is a second?

A second is a second long by definition, but if you measure any time in seconds, the number of seconds you infer will be subject to an error of at least $\mathcal O(10^{-15})$ because of the ...
Alwin's user avatar
  • 5,060
32 votes

Why do we use the electron volt?

Addressing only why it is used/useful in science today, not why or how it came about The other answers seem to come from a particle physicist's point of view; for a chemist the electronvolt is ...
pentane's user avatar
  • 3,022
32 votes

Why are "degrees" and "bytes" not considered base units?

Another answer (and a linked question) addresses the fact that that the SI derived unit for angles is the radian, which is a ratio of lengths. See e.g. The bit/byte question is interesting. In ...
rob's user avatar
  • 91.6k
32 votes
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Why is the length of the Kelvin unit of temperature equal to that of the Celsius unit?

Kelvins aren't really all that natural either; or rather, they are just as arbitrary as Celsius. You need another arbitrary quantity--the Boltzmann constant--to get the temperature unit to work with ...
Mark H's user avatar
  • 24.2k
32 votes
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Why is the Planck constant an exact number with defined value?

Planck's constant relates two different types of quantities, namely energy and frequency. That means it is a conversion factor which converts the units of quantities from one form to another. If the ...
flippiefanus's user avatar
  • 15.1k
32 votes
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What is a joule? I find the definition confusing

Maybe imagine the ball is being pulled by a weight, or a spring, back here on Earth. The weight falls down and pulls the ball along: It is easy to see that the weight goes down 1 meter when the ball ...
Stack Exchange Supports Israel's user avatar
29 votes
Accepted

Is there any truth to interpreting definition of a second as corresponding to oscillations?

You're correct and the video is mistaken. In fact, if cesium atoms were constantly oscillating between the two hyperfine states, cesium beam clocks wouldn't work at all! In its simplest form, a ...
hobbs's user avatar
  • 2,246
29 votes

Do units have to make sense in Physics?

Units in physics are units of the real world. They must be consistent, because the real world is. After choosing a definition of necessary fundamental units (as defined by the SI system e.g. - I am ...
Steeven's user avatar
  • 51.5k
27 votes

What's exactly the new definition of kilogram, second and meter?

The SI system is now defined entirely by physical constants. There are no more “prototype” artifacts. How it works is thus: https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-concise-EN....
Dale's user avatar
  • 103k
27 votes

Why is the Planck constant an exact number with defined value?

Before May 2019, Planck's constant was not defined by an exact value and instead was measured experimentally to be $6.626069934(89)\times10^{−34}\ \mathrm{J\cdot s}$. However, it is worth noting what ...
Sandejo's user avatar
  • 5,488
27 votes

What technology is needed for an individual to reproduce the current SI meter and kilogram from scratch?

I don't see any particular reason why you couldn't reproduce the Foucault experiment with bronze age technology. Foucault measured the speed of light to better than 1% - not quite the 0.1% requested, ...
g s's user avatar
  • 14k
26 votes

Why is the mole/"amount of substance" a dimensional quantity?

Tim, your reservations about the quantity called "amount of substance" is completely justified and many authors argue the same as you do. Let me expand some: "matter" or "substance" can be quantified ...
Vera K's user avatar
  • 575
26 votes
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Why is the mol a fundamental physical quantity?

The mole definitely isn't a fundamental physical quantity. It's just a shorthand for Avogadro's number, to make really big numbers more tractable. It's purely there for convenience, there's nothing ...
tparker's user avatar
  • 48.4k

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