210
votes
Accepted
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
$$T_{1/2}=\pi\sqrt{\frac{l}{g}}$$
$...
- 1,951
154
votes
Accepted
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 ...
- 46.3k
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 ...
- 26k
112
votes
Accepted
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--...
- 91.9k
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 ...
- 35k
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 ...
- 15k
80
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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 ...
- 16.2k
69
votes
Accepted
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 ...
- 129k
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 ...
- 560
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 ...
- 91.9k
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 ...
- 50.3k
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 ...
- 91.9k
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. ...
- 12.7k
44
votes
Accepted
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 ...
- 129k
43
votes
Accepted
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 ...
- 91.9k
43
votes
Accepted
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 $...
- 49.9k
38
votes
Accepted
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 ...
- 3,700
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 ...
- 7,117
36
votes
Accepted
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 ...
- 55.7k
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 ...
- 4,920
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 ...
- 4,072
32
votes
Accepted
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 ...
- 23.9k
32
votes
Accepted
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 ...
- 13.8k
32
votes
Accepted
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 ...
- 1,497
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 ...
- 2,972
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♦
- 85.2k
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 ...
- 2,181
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 ...
- 49.9k
Only top scored, non community-wiki answers of a minimum length are eligible