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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What's the unit of fine-structure constant? [closed]

What's the unit of fine-structure constant? I mean in SI units.
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34 views

Proving that Planck's Law is dimensionally homogeneous [closed]

I would like to know whether it is possible to show that Planck's Law is dimensionally homogeneous, as well as the steps taken to prove it. $$B_\lambda(\lambda, T) =\frac{2 hc^2}{\lambda^5}\frac{1}{ ...
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Dimensional inconsistency in first law of black hole thermodynamics

The first law of black hole mechanics (let's simplify by considering a uncharged and non-rotating black hole) can be written as $$\delta M = T \delta S$$ If I use the definition of Hawking ...
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1answer
23 views

Dimensional interpretation of inverse gradient length $\frac{d}{dx} \ln(Y)$

Preliminary definition: inverse gradient length Let me first explain what I mean by that term. The inverse gradient length of some quantity $Y$ (often thermodynamic temperature $T$) $L_Y^{-1}$ is ...
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1answer
266 views

Drag - Dimensional Analysis / Buckingham Pi

Dimensional Analysis / Buckingham Pi Theorem I'm working on dimensional analysis and I'm having trouble. Here's a problem from my book I'm working on for practice. I'm suppose to consider a small ...
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1answer
257 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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64 views

Functions and Length Scales

Regretfully I have to start with an apology as I fear I might be unable to express the question rigorously. Often reading physics papers the concept of "length scale" is used, in statements such as ...
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188 views

Why is the Fermi coupling constant always expressed in units of $(\hbar c)^3$?

Everywhere I've looked so far (such as NIST) the Fermi coupling constant $G_F$ is always expressed as $$\frac{G_F}{(\hbar c)^3} = 1.166 364(5) \times 10^{-5} \textrm{ GeV}^{-2}$$ never as just ...
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Pressure inside a typical white dwarf

Does any one know the order of magnitude of pressure inside a typical white dwarf (better with reference)? Thanks! I think it should be $m_e^4c^5/h^3$ (may be multiplied by $\pi$), which is $10^{22} ...
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1answer
65 views

Connection between the cosmological constant $\Lambda$ and the cutoff scale $\Lambda$

I'm trying to understand the connection between the $\Lambda$ from cosmology and the $\Lambda$ from QFT. Cosmology: The cosmological constant enters the Einstein equations. In the special case of the ...
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1answer
156 views

Moment of Inertia and Linear Dimensions

For similar solid bodies made from constant density, how does the Moment of Inertia about a particular axis vary with linear dimensions? This is from an school textbook. I have covered all of MI ...
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1answer
87 views

What defines a physical property? [closed]

The physical world around us has all sorts of properties, shape, color etc. If you move on to more complex systems, there are even more like some emotional properties etc. Why do we deem only ...
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Fundamental question about dimensional analysis

In dimensional analysis, it does not make sense to, for instance, add together two numbers with different units together. Nor does it make sense to exponentiate two numbers with different units (or ...
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Newton's Second Law of Motion

Newton originally wrote his second law as: "The rate of change of momentum of a body is directly proportional to the resultant force applied to the body, and is in the same direction as the force." ...
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How to get Planck length

I know that what Planck length equals to. The first question is, how do you get the formula $$\ell_P~=~\sqrt\frac{\hbar G}{c^3}$$ that describes the Planck length? The second question is, will any ...
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45 views

Why is one Telsa equal one weber per square meter instead of one weber per cube meter?

Lines of magnetic flux exist in three-dimensions, so how can they be measured per area unit?
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6answers
141 views

Dimension of an angle [closed]

Usually angles are described as dimensionless, justifying this by saying that they can be viewed as length divided by length. As a student of mathematics I'm asking myself wether this is a convention ...
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1answer
40 views

With radian as a unit, should action and angular momentum have the different units?

If one accepts radian as a fundamental unit, does it make sense that action and angular momentum have units differing in radian to the power of one? The same question applies for energy and torque. ...
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186 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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Dimensional analysis of explosive energy, no temporal element

I have a question about dimensional analysis, using the calculation of the explosive energy of the Bomb by Taylor in the 1940s as example. I am neither physicist nor mathematician so will have ...
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2answers
153 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
50 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
58 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 = ...
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1answer
61 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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Why does Coulomb's constant have units?

I think of Coulomb's constant as a conversion factor (not sure if this is correct). Kind of like how you would do calculations in kg and then times it by the conversion constant to convert your answer ...
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1answer
38 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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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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3answers
104 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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113 views

What in nature causes Newton's gravitation constant to have it's 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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Units of the Stokes-Einstein rotational diffusion coefficient

The Stokes-Einstein rotational diffusion relation tells us that we can write down a rotational diffusion coefficient for a sphere as: $$D_r \approx \frac{k_B T}{\zeta_f} \approx \frac{k_B T}{(8 \pi ...
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3answers
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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
37 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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116 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 ...
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110 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 ...
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1answer
43 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
109 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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2answers
30 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
25 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 ...
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141 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 ...
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1answer
79 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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3answers
451 views

Units INSIDE of a Dirac Delta function

I know that the units of a Dirac Delta function are inverse of it's argument, for example the units of $\delta(x)$ if $x$ is measured in meters is $\frac{1}{meters}$. But, my question is what are ...
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4answers
206 views

Natural unit conversion

I'm a bit confused about different notions of "natural units" that I encounter occasionally. I'm familiar with Planck units, and in particular I can understand the conversion between, say, metres and ...
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98 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
75 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
109 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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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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Primordial black hole mass [closed]

Use dimensional arguments to combine the fundamental constants $\hbar$, $c$ and $G$ to derive the least massive primordial black hole formed shortly after the big bang. I'm not sure how to combine ...
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1answer
47 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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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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90 views

Distance and velocity question

I know that speed is the derivative of distance. So integrating speed should give you distance. Let's suppose we have a speed which obeys this function: $$ v(x) = 2^{2^x} $$ So at time 0 the speed ...