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Questions tagged [dimensional-analysis]

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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Dimensional error

Wikipedia https://en.wikipedia.org/wiki/Semiconductor_optical_gain proposes the following formula for the material gain in semi-conductor: $$ g(\varepsilon) = \frac{\nu\mu_0^2}{4\pi\epsilon_0n} \...
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315 views

Explain Kerr-Newmann Black Hole Spins in SI Units

I'm trying to run some calculations on Kerr-Newman black holes, but I'm having two major difficulties. First, most equations I've been able to find are only for Kerr black holes. Second, essentially ...
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58 views

Why do all the uncertainty relations have the units of action?

After a good chunk of time today working with natural units on another project, and later walking and pondering on the uncertainty relations from quantum mechanics: is there any fundamental reason ...
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1answer
319 views

Dimensional analysis of the equation $s_{n}= u+ \frac{1}{2}(2n-1)a$

It is a question in my textbook to see if the equation $s_{n}= u+ \frac{1}{2}(2n-1)a$ is dimensionally correct where $s_{n}$ is the distance travelled by a uniformly accelerating body with initial ...
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4answers
711 views

How to express an energy in natural units

If I have some angular frequency e.g. $\omega [\text{rad } \text{s}^{-1}]$, I can easily express this as an energy as $E = \hbar \omega [\text{ J}]$. Now suppose I am working in Natural (Planck) ...
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2k views

Why can we only add or subtract things of the same dimension (meters/second, newtons, etc)? [duplicate]

Dimension analysis is a nice tool to create functions using physics dimensions that are desirable for our lives. I know, as an axiom, of sorts to me, that addition and subtraction must conserve units, ...
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324 views

Dimensions of charge in natural units

The natural units $$G = c = \hbar = k_{B} = 1$$ set fundamental constants of gravity, relativity, quantum physics, and statistical physics to simple numbers. However, surprisingly, the natural ...
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1answer
213 views

Dimensional analysis problem

I am asking this question here because i think this is fundamentally linked to physics as it revolves around around dimensional analysis and physical quantities. Background: Amount of substance is a ...
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1answer
460 views

Dimensional analysis vibration frequency of a star [closed]

I'm doing a classical mechanics course of the MIT on my own. In a problem set there is the following problem to be solved using dimensional analysis: "Derive an expression for the vibration ...
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1answer
169 views

Using dimensional analysis to find the expression for free energy

In page 181 of Thomas Hartman's notes on Quantum Gravity and Black Holes, we have the following: The thermodynamic free energy $F$ is given by $$F = - T \log Z,$$ where $Z$ is the partition ...
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1answer
233 views

Neutral D meson decay widths from dimensional analysis of feynman vertices

I know the decay width of a process is proportional to the interaction strengths at the vertices, and for a $D^0\to \pi^+\pi^-$ where $D^0=\bar{u}c, ~ \pi^+=u\bar{d}, ~\pi^-=u\bar{d}$, the decay ...
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2answers
448 views

Are space and time interchangeable?

There was a previous question asked that I don't understand (nor did many other people apparently). My question is hopefully different. On a Wikipedia article about speed of gravity it states: ...
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52 views

Issues reading a paper about batteries

I am looking for answers regarding a paper I am reading right now. I either found stupidly high values or strange SI unit. This paper is about battery charging, and the battery model used brings me ...
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1answer
9k views

Dimensions of electric charge

I was studying dimensional analysis, which is a technique used in conversion of units, checking the homogeneity of equations and also sometimes deriving unknown equations, if we can guess the factors ...
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1answer
131 views

Physical quantity that can be expressed using multiple fundamental units [closed]

Any physical quantity can be represented as a product of powers of fundamental SI units.For example, Force has dimensions $[\text{kg}\ \text{m}\ \text{s}^{-2}]$ and has three fundamental units. ...
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1answer
395 views

Statistical Mechanics: “Pressure” in a one-dimensional quantum system

For statistical mechanics homework I have to solve this problem: Consider a single quantum-mechanical particle in an infinite one-dimensional well of width L. From elementary quantum mechanics, ...
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1answer
436 views

Is there a difference between joules of energy per coulomb and volts?

There is a question in my textbook: A current of $7\ \mathrm{A}$ goes through the heating element in a hair-drier. The voltage of the heating element is $240\ \mathrm{V}$. b) How many joules ...
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1answer
47 views

Generalized Euler substitution doesn't seem to work when the integration variable has a dimension

I came across Euler substitutions while trying to evaluate the integral $\int \frac{y^2}{x^2+y^2+z^2 + x\sqrt{x^2+y^2+z^2}} dy$, where $x, y, z$ are length quantities. The generalized substitution at ...
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2answers
56 views

Dimensional analyse of charge quantity

F=m*a so dimension of F is [$M*L/T^2\\$]. $F = (G*M*m)/r^2\\$ $F = (k*q*Q)/r^2 \\$ Is it right to think that dimension of (q) is same with (m)?
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Is the gravitational acceleration 9.8 m s$^{-1}$?

I'm really new to science and physics so I apologize in advance if this question is too easy to be asked on this site. I'm retaking high school physics and and I'm using a site that claims covers the ...
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163 views

Amplitude of a single mode quantized light field in a cavity

When a single mode light field in a cavity is quantized, how is the amplitude of the field obtained? Is the dependence of the amplitude on parameters like cavity volume and frequency of radiation ...
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2answers
1k views

Units for dimensionless quantities

Do dimensionless quantities have units or not? I am confused a bit about this concept.
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1answer
117 views

What units does $x-y$ have if $x$ and $y$ are in °C?

So in equations (for example $Q=mc\Delta T$) one normally has °C divided by °C, giving a result with no temperature units in its dimensionality. So, does °C $-$ °C also give a result with no ...
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1answer
63 views

Units of Quantum States

I've been taught that a continuous quantum state $ | \psi \rangle $ is unit-less, while the (improper) kets $ | x \rangle $ have units of $1/\sqrt{length}$. I've seen a lot of relations that "force" ...
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2answers
194 views

Trying to understand acceleration from gravity force

I have to understand the classic formula for finding acceleration due to gravity's force. $$ \frac{GmM}{d^2} = m\times9.8\,\mathrm m /\mathrm s^2 $$ dividing the mass of the object out . . . $$ ...
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1answer
242 views

Prove gravitational constant $G=1$ in geometric units

I've seen that often geometric units are defined by setting $G=c=1$, however, I have been working with a different definition, namely, to multiply time in seconds by $c$ so that it's measured in ...
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126 views

How to apply dimensional analysis to solve the problem? [closed]

There is no question here now as the question was completely misleading. You can click here to see some questions?
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1answer
40 views

Is 0 of anything the same as 0 of any other thing? [duplicate]

So, we know that in physics, units matter. 2 cm is different from 2 newtons which is different from 2 seconds. But what if the number is 0? Is 0 of any unit the same as 0 of any other unit?
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3answers
50 views

Regarding dimensions

As the title states, my question is regarding dimensions of a physical quantity. My question is, can the exponent of dimension of a physical quantity be a fraction? I came up with this question ...
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1answer
106 views

Can we determine the numeric sign of proportional constant using dimensional analysis? [closed]

is it true or false can we determine the numeric sign of proportional constants in a physical equation using dimensional analysis?
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1answer
205 views

How do I convert Nm/Kg in MGOe? [closed]

i have to buy a few magnets of a certain attraction intensity, i would like to know how to convert Nm / Kg in MGOe. What is the formula? Can you please make an example for 100 Nm/Kg?
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1answer
750 views

What is the spacetime unit?

So we have a graph of space vs. time, space being $y$, time being $x$. What's the unit for the distance between them? $$\sqrt{(y m)^2+(x s)^2}$$ $$\sqrt{(3m)^2+(4s)^2}$$ $$\sqrt{\frac{(3m)^2}{(3 m)^...
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1answer
536 views

Force F is given in terms of time t and distance x by F= A \sin Ct + B \cos Dx. Then dimensions of A/B and C/D are? [closed]

I tried this problem for while day but i don't get it . I want the method of solving it
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1answer
374 views

Units of Einstein-Hilbert Action

Action is a quantity with units energy $\times$ time $=[kg \frac{m^2}{s}]$. The Einstein-Hilbert action is \begin{equation} S_{EH}=\frac{c^4}{16\pi G}\int \sqrt{-g}R d^4x \end{equation} Looking only ...
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1answer
110 views

Can I use the concept of dimensional analysis in problems of vector analysis?

For example if I have Gauss' law: $\nabla D=\rho_v$ how can I get one side from the other dimensionally? Same question goes for rotation and generally for operators. Please explain downvotes if there'...
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2answers
101 views

Units and Dimensions

Recently I came across a question where they have asked which of the options is a unit of power. It had both kVA and kW in options. My teacher told me that the former is used as per rating ( ...
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100 views

What is the meaning of non-integer powers of physical units in electrodynamics? [duplicate]

In the gaussian system the unit of the charge is the statcoulomb (statC), defined as $$ \mathrm{statC =dyn^{1/2} cm= cm^{3/2} g^{1/2} s^{−1}}$$ to be consistent with the fact that the Coulomb force is ...
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1answer
167 views

A unit that is not coherent?

"Derived units are defined as products of powers of the base units. When the product of powers includes no numerical factor other than one, the derived units are called coherent derived units" I know ...
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2answers
182 views

How do I decide dimensions of a logarithmic function?

How do I decide the dimensions of a trigonometric quantity and a logarithmic quantity? For example, what are the dimensions for: $$\frac{C}{B} = \frac{D^2}{A} + \log \left(\frac{AC}{BD}\right)$$
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320 views

Are increases in Planck's constant and the speed of light operationally distinguishable? [duplicate]

If only dimensionless constants are physically meaningful, and both Planck's constant, $h$, and the speed of light, $c$, are in the denominator of the expression for the fine structure constant, $\...
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774 views

Why is the string length around the Planck length?

In string theory, it is assumed that a string is about the size of a Planck length, $$\ell_{string} \sim \ell_{Pl} \simeq 10^{-35}\,\text m.$$ Why that length? Why not for example a hundred times ...
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1answer
146 views

Is pressure the derivative of viscosity?

I noticed the units for viscosity are $\left(\frac{kg}{m \cdot s}\right)$ and the units for pressure are $\left(\frac{kg}{m \cdot s^2}\right)$. Are these related in any way? Is there another ...
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1answer
233 views

Why do we write $t$ as $ct$ in special relativity? [duplicate]

We commonly write 4-vectors as $x=(x^0,x^1,x^2,x^3)$, where $x^0=ct$ rather than $x^0=t$. The only reason I can think of why this was done is to write everything in spatial dimensions. That is ...
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How to scale up a boat design?

I've been trying to research how to scale up a boat design. Specifically I am trying to find out how much power will be needed to "drive" the boat? Suppose I know that a 250 mm model boat, with 100 W ...
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1answer
426 views

Estimating the yield of the Trinity Test using dimensional analysis

So essentially I'm trying to re-do what G.I. Taylor did to estimate the energy released by the Trinity Test using dimensional analysis. I understand all of the dimensional analysis aspects, I'm just a ...
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1answer
68 views

Electrostatic Potential

Suppose I am given a charge density $\rho(x)$. Poisson's equation states that $$\frac{d^2\phi}{dx^2} = -\frac{\rho}{\epsilon}$$ Is there a simple way to see what the characteristic strength of the ...
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1answer
163 views

What does “dimension” mean in physics? [closed]

Still I don't get what's the difference between dimension and quantity. Are they same or they are different?
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1answer
131 views

How to properly define the physical dimension (unit) of a variable?

Let's say we have an equation like $$v=s/t.$$ I've come across multiple ways to define the units belonging to each variable: $(v/(\mathrm{m}/\mathrm{s}) = (s/\mathrm{m})/(t/(\mathrm{s}))$ $v_\mathrm{...
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2answers
3k views

What unit does $\Delta x$ have in the uncertainty principle?

Can somebody tell me how the units work out in Heisenberg's principle equation? Mass in $kg$ and velocity in $m/s$ cancel partially with Planck's constant, so what kind of unit is given to $Δx$ to ...
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2answers
3k views

Viscosity of ideal gas from dimensional analysis

Summary From dimensional analysis I find that the dynamic viscosity of an ideal gas must depend on its pressure $p$, density $\rho$ and mean molecular free path $l$ in this way: $$ \mu = C \sqrt{\...