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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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Why is the speed of light used to define the fourth axis of spacetime?

The four axes of spacetime are $x, y, z$ and $ct$, where $c$ is the speed of light, and $t$ is time. Why is the speed of light (not any other speed) used to define the fourth axis of spacetime? If ...
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1answer
33 views

Converting $\mathrm{ps/nm}$ to $\mathrm{ps}^2$

I have a dataset in the unit $\mathrm{ps/nm}$ for many different $\lambda$ which I want to convert to $\mathrm{ps}^2$. I guess I can assume that I only deal with Gaussian bandwidths such that $1\ \...
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0answers
25 views

Dimensional Formulae

Reading Bridgman's Applications to Theoretical Physics, I found a discussion on dimensional analysis where the charge of an electron is expressed in terms of mass, time, and length. What did he mean ...
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0answers
32 views

What are the units for state vectors in QM? [duplicate]

Specifically, it seems that a state vector should be dimensionless because: $| \langle \psi | \psi \rangle |^2$ is a probability which is dimensionless However, I find myself doing manipulations ...
0
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1answer
43 views

Meaning of units in the Heisenberg Uncertainty Principle

So we have the inequality $\Delta x\,\Delta p\geq \hbar/2$ Why is the uncertainty of position in meters? Isn't uncertainty measured in probabiliies? Does it make sense to say that the uncertainty in ...
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4answers
2k views

Is a unit vector really unitless and dimensionless?

According to my textbooks, a unit vector has no units and no dimensions, but is only used to specify direction. It only shows the orientation of a corresponding vector in space. I think it's true, or ...
30
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2answers
3k views

Are the units of energy the same in higher dimensions?

In 3 spatial dimensions, $$[E] = [ML^2 T^{-2}]$$ Would it change in higher dimensions? If yes, then what would be the dimensions for 4 spatial dimensions?
0
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1answer
65 views

In the value of gas constant $R$, what kind of mole is it?

Wikipedia gives $$R=8.3144598(48)\, \rm J\,mol^{−1}\,K^{−1}$$ But I want to ask how is it possible to write $\mathrm{mol}$ without a suffix? I mean, we must determine if we have $1\ \mathrm{mol}$ of ...
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1answer
49 views

What do we mean, concretely, by the unit $\rm N\:m$ (newton $\cdot$ meter)? [duplicate]

What do we mean, concretely, by the unit $\rm N\:m$ (newton $\cdot$ meter)? For example, $1 \:\rm m/s$ mean that each second, we make one meter. Also, $1\:\rm m/s^2$ mean that each second the speed ...
1
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1answer
69 views

Dimensional correctness of equations [duplicate]

I have studied that a dimensionally correct formula/equation may or may not be correct. But in order for a formula or an equation to be correct, it must be dimensionally correct, according to the ...
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1answer
34 views

Issue in conversions from force to mass units

I have a problem converting force to mass units, in this example for 9.81kgf: To get the mass, dividing by gravity, I get 1kg ...
0
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1answer
55 views

Conversion between mass units

I am enrolled in a course related to physics, and converting between mass units is so tricky for me. I always treat in my work only in SI units and maybe MKS units, at level of weights, I find it easy....
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1answer
70 views

mathematically explain why add operators with different physical unit is wrong?

Suppose I have two operators $J^2$ and$J_z$ where they represent the length of angular momentum and its $z$ component respectively. Sure, it's legal to write new operators like $J^2-J_z^2$ or $J_x+...
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1answer
38 views

Dilatations and action on derivatives of fields

How do derivatives of fields transform under dilatations? Specifically I am interested on what I misunderstand with the example: Consider a theory that has a field $A_\mu$ that transforms under ...
4
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2answers
89 views

How can momentum and position be combined into a phase space when they have different units?

Elaboration of the question: What is the geometrical interpretation of units? As in, a unit of length is a choice of scaling of the coordinate systems i.e. it is a choice of diffeomorphism, but then ...
3
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2answers
63 views

How do I add measurement units to a power-function relationship like $y = 0.17x^{0.52}$?

I have the equation $y = 0.17x^{0.52}$, where the units on $x$ are $\rm cm$ and the units on $y$ are seconds. I can't figure out how to put units on the constants so that they work out and I get the ...
0
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1answer
72 views

I'm confused about electric flux?

In a previous physics class, I learned that the electric flux was $\vec{E}\cdot\vec{A}$ (dot product), and hence the unit is $Nm^2/C$. But in my electromagnetics book, it says the unit is Coulomb, and ...
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4answers
169 views

Dimensional analysis of classical action

Hamilton's action for classical systems has the units Joule seconds ($\rm J\cdot s$), which in base units is $\rm kg\:m^2/s$. Does the $\rm m^2$ have anything to do with area? I'm having a hard ...
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1answer
48 views

Is this a valid argument for the dimensions of this integral? [closed]

Given the integral: $I = \int_{-\infty}^{\infty} x^{2n}e^{-\alpha x^2} dx$ If I say that if: $$[I] = [L]^{2n+1}$$ And the dimensions of alpha must be $\frac{1}{[L]^2}$ since the exponent must be ...
1
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1answer
51 views

How to handle dimensional analysis under exponents

Say there is a river of saline solution and I want to measure the flux of salt. That is, I want to measure the miligrams (mg) of salt per second ($\sec$) passing through a square centimeter area (cm$^...
0
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2answers
63 views

What is the dimensional analysis of the position?

My teacher gives me an equation for the position of a particle to analyse the equation by the dimensional analysis method: The position of a particle moving under uniform acceleration is some ...
1
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1answer
42 views

Can this quantity defined by exponentiating lengths be meaningful?

I just read Accurate predictions of coexistence in natural systems require the inclusion of facilitative interactions and environmental dependency in which they defined the following property:$^1$ $$\...
0
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1answer
28 views

Possible fundamental dimensions in Pi Buckingham theorem

While the Pi Buckingham is often taught in a fluid dynamics context, in which the relevant fundamental dimensions are generally : Mass, Length, Time and Temperature, it can obviously be applied to ...
0
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1answer
41 views

Non-dimensionalization of Navier-Stokes equations multiphase flows

I am currently dealing with multiphase flows and have to use the non-dimensional form of the Navier-Stokes equations (NSE). In the scientific literature I found various formulations (and almost no ...
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3answers
31 views

Whats the dimension of no of molecules per unit volume

I know its trivial but still i am confused,i know that no of molecules per unit volume (n) is dimentionless but my confusion is what if we describe it by total number of molecules by total volume(n=N/...
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0answers
52 views

Non-spreading wave packets

I am reading an article (Nonspreading wave packets, by Michael Berry, Am. J. Phys. 47, 264 (1979), author eprint), and I have some questions about the maths within. First of all they take a wave ...
2
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2answers
1k views

Why are the dimensions of escape velocity correct?

How does this formula work, from a dimensional analysis perspective? $$ v_\text{escape} = \sqrt{\frac{2GM}{R}}$$ The way I'm thinking about it is that $G$ is in units $\text{N} \cdot \text{m}^2/\...
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2answers
83 views

How to put $c$ back into relativistic equations?

Many books set the speed of light $c=1$ for convenience. For example, Weinberg in his textbook "Gravitation and Cosmology" (though $G$ is still left as a constant): $$\begin{align} \mathrm{d}\tau^2 &...
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0answers
44 views

why we can use dimensional analysis to discover formulas?

if I want to discover the time duration ($t$) of a object falling from an heigh ($h$) to the ground in a gravitational field ($g$), I can guess that $t$ is proportional to $h, g$ and the mass ($m$). ...
2
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1answer
66 views

Dimensional analysis of vectors, possible?

Usually we use dimensional analysis to find the dimension of acceleration or force, but can we do the same thing to find the dimension of the vector acceleration, and the vector force, or we can't ...
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2answers
96 views

Question about Radian as a unit

I'm having a hard time trying to understand the units between angular velocity and basic velocity of a circle. For angular velocity the units are Radian(s) per second(s) or degree(s) per second(s). ...
3
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2answers
86 views

Is the International System of Units complete?

Are there any known (measurable continuous) physical quantities, which are neither base quantities of SI, nor are derivable from the base quantities? In other words, are there any quantities which ...
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3answers
44 views

Scaling of force between cubes? [closed]

I found an interesting problem online which has been confusing me for quite a while. Basically, two solid cubes of side length $a$ touch each other along one of their faces, and I am to find how many ...
0
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1answer
55 views

Does it make sense to multiply a unit by a negative number?

I was thinking about the way our system of units of work, and I realized that we have been multiplying units (such as for lengths) by negative numbers, when dealing with vector quantities; positive ...
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3answers
50 views

Magnetic $H$ field unit in cgs system

I'm studying an old E&M textbook which uses cgs unit system. I'm re-writing the formulas in SI unit. The book says $\vec{H}=\vec{B}-4\pi\vec{M}$. So I guessed that $H$ should have same unit as $...
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4answers
102 views

Why does this paper use 1/cm for units of frequency?

Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency. Here is an excerpt: It doesn't seem like wave number, as they clearly call it frequency. What's going on here? $^*$ ...
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2answers
60 views

Infinite plane gravity: what is “mass density per unit area”?

Recently I learned that the gravity of an infinity plane is independent of the distance from that plane. In fact it is $$g = 2\pi G \sigma$$ where $\sigma$ is "the mass density of the plane per unit ...
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1answer
81 views

How can we use zero in physics [duplicate]

Is better to say the e.g. kinetic energy is 0 joule or kinetic energy is 0 ? since 0*joule equals 0.Is a mathematical concept behind because in many books i find both ways.
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1answer
58 views

Height of a water tower, using Pascal's Law [closed]

This is a problem on Brilliant.org which asks, if you want to receive 400kPa of water pressure to a house that is at the foot of a water tower, how tall must the water tower be? It provides you with ...
0
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0answers
47 views

Why are the Planck charge and Planck mass values so much larger than observed particles? [duplicate]

The Planck charge and mass values seem rather unusual. Is this an indicator that there is a lack of understanding in current theory, or is there a logical explanation for the magnitude of these two ...
0
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2answers
65 views

Keeping track of units

I'm not quite sure how keep track of physical units when differentiaion is involved. I find it important to keep track of units because I want to be able to check the units afterwards. I will discuss ...
3
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4answers
1k views

How do we recover units of force from units of gravitational potential?

The gravitational potential $G_\text{pot}$ has units of energy per unit mass: $$ \bigg[\rm\frac{J}{kg}\bigg] = \bigg[\rm\frac{kg\cdot m^2}{s^2\cdot kg}\bigg] = \bigg[\rm\frac{m^2 }{s^2}\bigg]. $$ ...
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1answer
106 views

Why we can't multiply two extensive quantities together?

I have read that regarding the equation of state $PV=nRT$, since $V$ is an extensive quantity $P$ should be an intensive one because the product of extensive quantities is inherently non-linear. ...
2
votes
1answer
77 views

Biot number - Heisler chart correlation

Hello I have a question about Biot number. I know that if Bi > 0.1 we're using Heisler chart to calculate heat transfer else Lumped capacitance method can be used. However can we use Heisler chart Bi &...
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2answers
62 views

How to interpret resistivity and its unit?

I was wondering which interpretation could we find for the resistivity, what image correspond to the concept. Furthermore, how to interpret its unit $\Omega \:\rm m$ . Why is it more logical than a $ ...
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0answers
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In non-dimensionalization, what does it mean when one “assumes” a quantity has been scaled relative to another quantity?

I'm trying to replicate the results of a paper, and they use the quantity $l$ to denote the length of the recirculation zone behind a cylinder for a problem regarding fluid flow past a cylinder. Early ...
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3answers
527 views

What is the unit for work done?

My textbook's equation for work done is: work done = force * distance So this means that the unit should be Nm. However, when I researched on Google, a lot of people were saying that the unit is J....
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4answers
2k views

Is dimensional analysis valid for integrals

Can we apply dimensional analysis for variables inside integrals? Ex: if we have integral $$\int \frac{\text{d}x}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{-1} \left(\frac{a}{x}\right),$$ the LHS has no ...
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1answer
68 views

Converting GPa and TPa to N/m

I have a problem with converting units, in some papers, ultimate tensile strength has been shown with GPa or TPa, but in some papers, it has been presented with N/m. (not newton per square meter) As ...
2
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1answer
144 views

Mass Dimension of derivative in a Lagrangian

What is the mass dimension of the derivative $\partial$ in a Lagrangian? I am really confused about this. I read somewhere it is 1 and another place I saw it is -1. Please could someone clear this ...