Tagged Questions
7
votes
5answers
139 views
Physical representation of volume to surface area
I was looking at this XKCD what-if question (the gas mileage part), and started to wonder about the concept of unit cancellation. If we have a shape and try to figure out the ratio between the volume ...
0
votes
1answer
38 views
The units of gain and number of atoms in population inversion in a laser
I am following my university course notes on amplification in laser media, and have come across expressions for the gain of a medium, but the notes are not exactly rigorous... The expression given for ...
3
votes
1answer
154 views
What are units actually?
This question is about the concept of units in physics.
Firstly - do units have a formal mathematical definition? How are they different from pure numbers? Are pure numbers defined to be ratios of ...
3
votes
5answers
545 views
Does the unit of a quantity change if you take square root of it?
For example, I have a mass, m = 0.1kg and I square root it, giving me m = 0.316 (3s.f.) does the unit still stay as kg, or does it change?
3
votes
1answer
78 views
Units for physical constants
Someone told me that units for $G$ and $\epsilon_0$ (gravitational constant and Coulomb's constant) are placed there simply to make equations work dimensionally and that there is no real physical ...
2
votes
3answers
71 views
Curious relation between the dependance in ℏ of Planck units and units dimensions
Looking at Planck units, there seems to be a curious rule between the dependance in $\hbar$ of a Planck unit and the unit dimensions of the corresponding physical quantity.
Let the dimensions of the ...
0
votes
3answers
159 views
Temperature in CGS (Gaussian) units
I've been struggling with conversion from Gaussian to SI units for sometime, trying to figure out how derived units in CGS (current, charge etc) relate to the SI units.
But I couldn't find any ...
1
vote
2answers
168 views
Showing that position times momentum and energy times time have the same dimensions
I've been asked to show that both the position-momentum uncertainty principle and the energy-time uncertainty principle have the same units.
I've never see a question of this type, so am I allowed to ...
2
votes
3answers
276 views
Planck time, distance, mass? Why do we take those values?
Say we want to make an educated guess for critical values of time, distance and mass, where quantum gravity effects are supposed to be non-negligible. These values are given the prefix "Planck-". Now, ...
0
votes
2answers
82 views
Dimension analysis of de Broglie equations
One form of one of the de Broglie's equations is this:
$\lambda = \frac{2\pi\hbar}{p}$
Units:
$\lambda = [m]$
$\hbar = [Js]$
$p = [\frac{kg m}{s}]$
$J=[Nm]$
How can one show with dimension ...
0
votes
3answers
94 views
How could the unit of a constant be unit of tension $N^{-1}$?
From my pervious Question:What are the units of the quantities in the Einstein field equation?
i noticed that the unit of this constant $\frac {G}{c^4}$ is the unit of tenstion
$$\frac ...
4
votes
2answers
305 views
What are the units of the quantities in the Einstein field equation?
The Einstein field equations (EFE) may be written in the form:
$$R_{\mu\nu}-\frac {1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\frac {8\pi G}{c^4}T_{\mu\nu}$$
where the units of the gravitational constant $G$ ...
4
votes
1answer
683 views
What are the units or dimensions of the Dirac delta function?
In three dimensions, the Dirac delta function $\delta^3 (\textbf{r}) = \delta(x) \delta(y) \delta(z)$ is defined by the volume integral:
$$\int_{\text{all space}} \delta^3 (\textbf{r}) \, dV = ...
5
votes
7answers
700 views
Why are radians more natural than any other angle unit?
I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
3
votes
1answer
172 views
Question about units in Lagrangian dynamics (inertia matrix)
I have a 3 degree of freedom system and my equation of motion is like this:
$$M(q)q_{dd} + C(q,q_d)q_d+G(q)~=~0$$
$M(q)$: inertia matrix
$C(q,q_d)$: Coriolis-centrifugal matrix
$G(q)$: potential ...
0
votes
1answer
251 views
Understanding units and the units of the derivative operator
Suppose that $f$ is a function from unit $A$ to $B$, then what is the unit of $f'(x)$?. We can do $f'(x)\Delta x$ to get an estimate of $f(x + \Delta x)$. Since the latter has unit $B$, so has the ...
0
votes
3answers
85 views
Is it possible to be changed Energy Unit in future or it is strict reality in nature?
Could you pease tell me why energy unit must be $Energy=Mass . \frac{Distance^2} {Time^2}$? (I tried to write general form of Energy unit)
What is the strong proof of that unit? Does it just depend ...
1
vote
1answer
117 views
Working with atomic (?) units in solid state physics
I'm having some troubles understanding the units used in solid state physics paper. In the paper I read
$\Lambda a \sim 1$
where $\Lambda$ is a momentum cutoff and $a$ is the lattice spacing of a ...
1
vote
1answer
88 views
How to interpret the appearance of time units in the units of a physical quantity?
Or phrased more abstractly, how to interpret the appearance of time dimension $[time]$ in the dimension of a physical quantity?
For example, the dimension of pressure is $[mass] [length]^{-1} ...
7
votes
5answers
662 views
units and nature
I am wondering whether the five$^1$ units of the natural unit system really is dictated by nature, or invented to satisfy the limited mind of man?
Is the number of linearly independent units a ...
1
vote
1answer
464 views
Question Concerning Dimensional Analysis
In the first lecture of MIT's Classical Mechanics Professor Lewin talks about Dimensional Analysis.He talks about an apple being dropped from a certain height can be quantitatively expressed as the ...
13
votes
9answers
3k views
What is the logarithm of a kilometer? Is it a dimensionless number?
In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is.
Suppose I have something with length $L = 1 km$.
$\lg L = \lg km$
It ...
8
votes
3answers
549 views
Understanding counterintuitive units like s^2
One of the things I never understood but was too afraid to ask is this: how should I think of things like kg/s^2. What exactly is a square second? Square foot makes sense to me because I can see it, ...
