Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.

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243 views

Why is the action dimensionless in natural units?

As I understand it, a natural system of units is one in which the numerical values of $c$ and $\hbar$ are unity, i.e. $c=\hbar =1$. What I find confusing is that they are still dimensionful, i.e. $[...
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2answers
173 views

When are 2 quantities multiplied in physics? [closed]

5*3 = 15. We get 15 by adding five 3 times. Multiplication of 5*3 means adding 5 3 times.i,e multiplication is repetitive addition.Multiplication is perfectly defined in mathematics. $F= m*a$. If ...
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1answer
64 views

Calculus of Variations - Virtual displacements

I am currently reading "The Variational Principles of Mechanics - Cornelius Lanczos", in which the author talks about the variation of a function $F(q_1, q_2, \dots q_n)$ where $q_1, q_2, \dots q_n$ ...
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1answer
61 views

Non-dimensionalize Schroedinger's equation for this potential

I am having trouble non-dimensionalize this S.E. in order to solve numerically.. the potential is $$V(x)=-V_{0}/(1+x^2/L^2)$$ we know that $A = V_{0}/\hbar \omega$ is dimensionless, and $B = E/\...
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1answer
71 views

Visualizing Physical Units in Phyiscs

I do best in physics when I can make sense of the units that accompany values, and I do this by visualizing in my mind what is happening. Take for instance, $v=\frac{s}{t}$. When I think of velocity I ...
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1answer
48 views

Dimensions of $\phi$ in scalar field theory

On Srednicki page 90-91 (in printed edition) he derives that $$[\phi] = \frac{1}{2}(d-2) \tag{12.10}$$ from $${\cal L}=-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi -\frac{1}{2}m^{2}\phi^{2} - \...
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0answers
40 views

Equations of above three variables cannot be solved with dimensional analysis. What does that mean?

I came across this statement while Googling about dimensional analysis. At first I thought that I understood what the statement meant, but now I realize that I really have no idea. What does the ...
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5answers
165 views

What in nature causes Newton's gravitation constant to have its given value?

Does the value of Newton's universal gravitational constant $G$ remain a mystery? Why does it have the value that it has?
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3answers
111 views

Power statement is valid for MW Or KiloWatts? [closed]

If I can talk to someone and tell him that a new power plant inaugurated by Prime Minister will produce $60$ megawatts per hour, will it be true to use $\mathrm{MW}$ unit for Power?
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3answers
58 views

Why are measurements standardized the way they are?

Using meters as a base length, squaring or cubing lengths smaller than 0.67m makes the square term larger than the cubed term. This fact causes certain properties of physics (how rain needs to form?) ...
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1answer
44 views

Converting $W/m^2 $ unit [duplicate]

In my equation I have a unit measured in MET found here $1MET=58.2 W/m^2 $. But my other parameter which is metabolic heat generation is measured in $W/m^3$ . I want to convert $W/m^2$ units ...
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3answers
118 views

Does this dimensioneless quantity have a name?

When studying creeping flows, a common choice for a characteristic pressure scale is $$p_0 = \frac{\mu_0 U_0}{L_0},$$ where $\mu_0$ is a reference dynamic viscosity, $U_0$ is a reference velocity and $...
2
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3answers
130 views

Are the 7 base quantities in SI system really independent?

In a typical description of the 7 base quantities of the SI system we see the following two points: All other quantities can be derived from them. They are "independent". My question is about ...
3
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2answers
119 views

Is it a problem that you can write the logarithm of a quantity with units? [duplicate]

While working out something in thermodynamics, I encountered an equation that had a term like $\log(n_1/n_2)$, where, $n_1$ and $n_2$ are the number densities. Now of course the argument of the $\log$ ...
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1answer
61 views

Dimensional consistency of an equation

We know that if an equation has to be physically correct then it must be dimensionally consistent i.e. If an equation is not dimensionally correct then it can never be physically correct. Now in the ...
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2answers
33 views

Dimensional equation for measuring logarithm of volume

I have a measure that uses radiation dose (M.U. $Gray$) and $\log(Volume)$. The measure is $[\frac{Dose}{\log(Volume)}]$ that is $[\frac{D}{\log(l^3)}]$ with $D$ as radiation dose (M.U. unit is Gray) ...
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1answer
27 views

How to convert between units of heat capacity?

I'm supposed to convert the heat capacity of water in $\frac{cal}{g^oC}$ to the heat capacity in $\frac{J}{(Kg)(K)}$ I was able to convert it from 1.00$\frac{cal}{g^oC}$ to 4184$\frac{J}{Kg^oC}$, but ...
2
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1answer
92 views

Why did we make equations dimensionless? [closed]

I study a paper on propagation of plane wave, in which equations are made dimensionless. Equation of motion is \begin{equation*} c_{ijmn}u_{m,nj} = \ddot{u_i} \end{equation*} where $c_{ijmn}$ are ...
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2answers
163 views

Can a quantity have two units?

We know that Force has unit of newton and torque has unit of newton meter. Then if you define the energy, which has same magnitude of work then, $W=Fx$ has unit of Joule ( $J$ ) (or $Nm$ ) while $W=\...
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3answers
182 views

Physical interpretation of source term in wave equations

Let me start with an example. If we base our calculations on the Newton's second law without any further mathematical treatment, then our equation describes equilibrium of forces, i.e. it is of the ...
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1answer
76 views

Why does $v^2=cad$ by dimensional analysis rather than $v^2=ad$? [closed]

Constants are generally added in functions to adjust for when magnitudes don't contain information necessary to the accuracy of the equation. Why is it that $v^2=cad$ instead of $v^2=ad$? What ...
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1answer
144 views

How are the watt-second, the newton-meter and the joule different?

The joule is $\mathrm{kg\,\ m^2/s^2}$ right? The watt-second is $\mathrm{J/s} \times \mathrm{s}$ thus $\mathrm{J}$. The newton-meter is $\mathrm{kg \,\ m/s^2} \times \mathrm{m}$ thus $\mathrm{kg \,\ ...
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1answer
50 views

Books or other sources for natural units, Planck units, dimensional analysis etc. for someone with only high-school physics knowledge

I'd like to know more about natural units, Planck units, dimensional analysis, etc., and things like how units are "created" by man or by the universe, universal constants and where they come from. ...
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1answer
64 views

Units of Velocity Components and Metric Tensor Components

I was watching a GR lecture on youtube, and the speaker explains that the units of the components of velocity are $[v^{\alpha}]=\frac{1}{T}$, the metric tensor has units $[g_{\alpha\beta}]=L^2$, and ...
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56 views

How to compare dimension of this with velocity [closed]

Prove that the dimensions of $\large \sqrt{\frac{1}{με}}$ are that of the velocity?
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1answer
296 views

What is meant by 'probability of transition per unit time'?

Today I came across a term used by Feynman in his thirteenth lecture: 'probability per unit time' to go from $| 1\rangle$ to $|2\rangle$ while initially being at $|1\rangle$. This is the excerpt fom ...
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0answers
26 views

Effective Medium

Please consider the following problem : A plane wave of wavenumber k is incident on an infinite slab which is inhomogeneous in the z direction. Also assume harmonic time dependence and that the ...
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2answers
1k views

Dimensional or dimensionless constant

While deriving new equations , how do theoretical physicists know whether the proportionality constant in their equation will be dimensional or dimensionless? I mean, say for example, we consider ...
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0answers
77 views

How to make two equations dimensionless? [closed]

I recently got set this problem and am having trouble scaling the resulting equations. Any help would be appreciated. An incompressible thermal conducting fluid is contained between two infinite ...
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4answers
2k views

What happens to the units when squaring a variable?

What happens to the units of a squared variable? For example, if I squared velocity, would the units, metres per second (${\rm m}/{\rm s}$), change as well?
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2answers
82 views

Dimensional analysis - When can you introduce constants that make dimensions compatible?

I have just read this question: What justifies dimensional analysis. One statement was: Maybe the speed of a comet is given by its period multiplied by its mass. Why not? As a formula this is $...
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3answers
195 views

Given the Newton constant $G$, the speed of light $c$ and the Planck constant $h$, construct an energy of the system [closed]

How do I use dimensional analysis to construct an energy for the system given the Newton constant $G$, the speed of light $c$ and the Planck constant $h$? I don't know of any energy formulas ...
3
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2answers
272 views

Can you express mass in other dimensional units?

I'm just started a Physics I course, and while I've paid attention, I'm stuck on one of the first problems: Express mass ($M$) in terms of acceleration($a$), density($D$), area($A$), and time($t$). ...
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3answers
96 views

Does the ratio of thermal energy to planck's constant have physical significance?

I realized that I had never noticed that $\left[ \frac{\hbar}{k_B T} \right]=$ Time. At $T \approx 300 K$, we have $\frac{\hbar}{k_B T} \approx 10$ fs. What, if anything, does this quantity mean? Does ...
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1answer
395 views

Scaling arguments and derivatives

I am trying to understand scaling arguments. Imagine one has a physical theory described by an equation whereby the first (spatial) derivative of a quantity, say $G$, equals the second (spatial) ...
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5answers
130 views

What forms can units take?

They have stated in my physics book that all units can be made by combining SI base units. I have got a few question about this. Can we raise one unit to the power of another unit? For instance: ${...
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0answers
28 views

Dimensional Analysis of tunnelling current expression

I have been racking my head trying to get the units to work on an expression for 1D tunnel current through a potential barrier. This expression is straight from S. Sze's "Physics of Semiconductor ...
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3answers
268 views

Drag force - dimensional analysis

I have tried the following example from the link: MIT OCW 8.012 PS1 It is about dimensional analysis. Derive an expression for the drag force on a ball of radius $R$ and mass $M$ moving with ...
3
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1answer
343 views

When can two quantities be added together?

Whenever two things are to be added together, one typically needs to check whether this actually makes sense, and an addition is said to make sense, in principle, when the units match up. Yet, ...
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1answer
81 views

Expanding physical quantities in dimensionless parameters [closed]

I have a system with two dimensionful parameters, say, chemical potential ($ \mu $) and temperature ($ T $). Now I want to write down an ansatz for any physical quantity (e.g, Greens function) at ...
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1answer
131 views

physical meaning of dimensionless parameter

What does it mean when there is nor not a dimensionless parameter in my model? In quantum harmonic oscillator, we don't have dimensionless parameter while in hydrogen atom case we have one which is ...
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1answer
424 views

What is the difference between unit and dimensions?

If I say Height of a block = 2m, then would "Height" be called as a dimension
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5k views

Why are angles dimensionless and quantities such as length not?

So my friend asked me why angles are dimensionless, to which I replied that it's because they can be expressed as the ratio of two quantities -- lengths. Ok so far, so good. Then came the question: ...
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1answer
145 views

Relating period, volume, surface area and the velocity of sound by dimensional analysis

The question is:- There is a dimensional relation between period T, volume V, surface area A and the velocity of sound C. Assume that period increases with volume and decrease with increase in area. ...
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2answers
185 views

Do bras and kets have dimensions?

I'm trying to understand more intuitively what bras and kets are, but some aspects of them remain a mystery to me. We usually think of $\psi (x)$ as having dimension of $[1/\sqrt{L}]$ so that ...
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188 views

Exercises with solutions in dimensional analysis - reference request

I am currently trying to brush up on my skills in dimensional analysis, and computing with units. Is there a good source of worked examples, and exercises with solutions? I'd prefer to have solutions ...
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2answers
153 views

What does this equation mean? [closed]

So I have just entered 11th grade and started limits on my own but my Physics textbook has an equation which I don't understand, I suspect it uses integration which I haven't learned yet. So can ...
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2answers
248 views

Dimensional Analysis Question [closed]

First of, I would like to say that I have tried this question, and have my answer as well, just not sure such a method of obtaining the answer is valid or not, therefore trying to look for help here. ...
3
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1answer
261 views

Buckingham-$\Pi$ theorem application: the case of only 0 or 1 dimensionless groups?

In dimensional analysis, we might consider a problem like: $$ f(q_1, q_2, ..., q_{n-1}) = q_{n} $$ where $q_i$ are physical quantities of interest. In order to determine how many $\Pi$ groups can be ...
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1answer
177 views

Is the dimension “number of particles” a fundamental, or derived dimension (based on mass), or does it depend on the context, or is it dimensionless?

I consider "fundamental quantities" to be those that have dimensions that are are like length, mass, time, temperature, and so on. "Derived quantities" have dimensions that can be written in terms of ...