208 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
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153 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
112 votes
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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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110 votes
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Why is a second equal to the duration of exactly 9,192,631,770 periods of radiations?

That number, 9192631770, was chosen to make the new definition of the second as close as possible to the less precise old second definition. This means that--except for the most precise measurements--...
Farcher's user avatar
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100 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
87 votes

Do all equations have identical units on the left- and right-hand sides?

It doesn't matter where the equation came from - a fit to experimental data or a deep string theoretic construction - or who made the equation - Albert Einstein or your next-door neighbour - if the ...
innisfree's user avatar
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80 votes

Why is a second equal to the duration of exactly 9,192,631,770 periods of radiations?

It's a definition of a unit, which is an arbitrary choice. In the past we used to define a second as 1⁄86,400 of a solar day and later as "the fraction 1/31,556,925.9747 of the tropical year for 1900 ...
CuriousOne's user avatar
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69 votes
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What are the proposed realizations in the New SI for the kilogram, ampere, kelvin and mole?

So the BIPM has now released drafts for the mises en pratique of the new SI units, and it's rather more clear what the deal is. The drafts are in the New SI page at the BIPM, under the draft documents ...
Emilio Pisanty's user avatar
57 votes
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Why is the prospective new kilogram standard a sphere?

If you know the diameter of the sphere, you know everything you need to know about the dimensions. It all comes down to one single value. Any other shape requires multiple dimensions and thus ...
Adam Davis's user avatar
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55 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
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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
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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
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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
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42 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
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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
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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
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34 votes

Do all equations have identical units on the left- and right-hand sides?

It depends what you mean by "unit". If you mean something like "seconds", then no. Counterexample: 1 minute = 60 seconds has different units on both sides, but they're both ...
user541686's user avatar
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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
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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
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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 ...
user253751's user avatar
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31 votes

Why is the prospective new kilogram standard a sphere?

There is a nice article in the New Scientist that describes how these spheres were made. Sphere can be made very precisely (and their shape measured accurately) simply because of their symmetry - and ...
Floris's user avatar
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31 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
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31 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
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