Questions tagged [units]

Units are standards of measurement used for different types of quantities.

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Is there any reason why $N\ kg^{-1}$ shouldn't be used as the units for acceleration?

When doing a calculation involving a force of $F=1000$ N on a mass of $m=100$ kg we use the formula $a=\frac{F}{m}$ $$a=\frac{F}{m}=\frac{1000\ N}{100\ kg}=10\ N\ kg^{-1}$$ Is there any reason why I ...
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Does “$\rm m/s$” mean the same thing when used for instantaneous velocity and for mean velocity?

The following question on Philosophy SE https://philosophy.stackexchange.com/q/73366/ relies on this "given" "suppose that the instantaneous velocity of object A is $1$m/s and that the mean ...
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I understand weight is measured in kilogram force, do we have smaller units like gram force? [closed]

I have read the explanation on the platform the confusion on the units of mass and weight.
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What is 'alpha_L' in the Lorentz Force equation, and 'alpha_B' in Biot-Savart? In the cgs system? [closed]

While reading about the derivation of cgs units, I came across a constant or something in some variation of Lorentz's force law represented by a lowercase-alpha-underscore-capital-L. Then a similar ...
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Clarification of “inertial mass” explanation

I am currently studying Classical Mechanics, 5th edition, by Kibble and Berkshire. Chapter 1.3 The concepts of Mass and Force says the following: Clearly, we can compare the inertial masses of two ...
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99 views

Why does $\epsilon_0=1$ in CGS units?

This Wikipedia article gives a table of certain constants in different systems of units. I noticed that in Gaussian and electrostatic CGS the value of $\epsilon_0$ equals the dimensionless $1$. I ...
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1answer
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Converting units, for the magnetic moment

I found, that magnetic moment is measured by $\rm J/T$, and equals magnetization times volume: $$\vec{m}=\vec{M}V$$ Magnetization, also equals magnetic susceptibility times external magnetic field: $...
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Which physical qualities have only one unit of measurement?

Which physical qualities have only one unit of measurement? One example is frequency, Hertz. Are there others?
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What are the accepted abbreviations for Million Years and Billion Years?

I'm putting together some charts and the time axis in one shows billions of years, the time axis in another shows millions of years. I've seen in various publications $my$ and $myr$ (also $ma$) for ...
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Why is surface tension measured in units of milliNewtons per meter? Rather than square meter(s)?

Why is liquid surface tension written in units of mN/m, or milliNewtons per meter? The related concept of surface energy for solids uses units of milliJoules per square meter.
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Proving base Units of SI are not enough for numerical computations [closed]

I have been working on a way to prove that the base unit of SI is not enough for numerical computations to make sense. What I mean by that is let's say you're given units of angular velocity to be [1/...
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How do units 'change' when we move to the language of differential forms?

Consider a 2D Euclidean vector as we're taught in first year: $p = x \>\hat{i} + y \> \hat{j} $ where x and y are in meters. If one goes looking for the units of a unit vector they will be told ...
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Units of angular speed vs linear speed [duplicate]

I'm studying pendulums, and the units have me a bit confused. In a pendulum, Iw^2=mgL. Putting together the units of the left side of the equation, we get gm^2 (rads^-1)^2=g(m^2)(s^-2)(rad^2). But ...
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Units of the Boltzmann constant in $2$ dimensions

I am answering a question in which volume is given as $m^2$ which I assume means that the question is considering a $2$ dimensional box for the volume. I am trying to calculate $N$ using the given ...
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Confusion with units of angular velocity [duplicate]

I know that the SI unit of angular velocity is $s^{-1}$ (because radians or angle measure is dimensionless). I encountered a question that said: Given angular velocity = $12 \, s^{-1}$ and angular ...
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Why are luminous intensity, luminous flux and illuminance physical quantities if they are based on the sensitivity of the human eye?

If luminous intensity and other derived quantities are based on the luminosity function, which is based on the sensitivity of the human eye, why are they physical quantities? Why is luminous intensity ...
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Is there a need for the unit mole? [duplicate]

If 1 mole of X is approximately $6.02 \cdot 10^{23}$ X, why is it a unit? How does it have the characteristics of a unit? Is it just a different way of writing the Avogadro's constant? Does amount ...
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Is there a use of the SI units gray, sievert and katal in pure physics

Since the gray and the sievert are associated with relative biological effectiveness of the radiation and the katal is associated with catalytic activity, do the gray (Gy), sievert (Sv) and katal (kat)...
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Converting the Gravitational Constant [closed]

Hello all and thank you for reading. I am creating a program in Unity where I recreate the earth-moon orbit. Unity struggles with numbers so large when I write code in meters and kilograms so I made ...
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Convert SI units into natural units

I have a simulation program which uses cgs-units. Additionally, I defined a natural system of units: \begin{align} \text{L} = [R], \quad \text{M} = \left[ \frac{e^2}{p^2 R^9} \right], \quad \text{T} =...
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Calculating the units of pressure in General Relativity, knowing $G=M=c=1$

I'm trying to figure out how large Pressure units compared to the standard CGS model is when taken $G=M=c=1$ What I have been thinking is: $$\dfrac{GM\rho}{r^2} = - \nabla P$$ or $$\|G\| \mathrm{\...
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3answers
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Can the argument of a function contain physical units?

Consider the function of temperature as a function of position, $T(x,y,z)$. Is the argument of the function dimensionless? I mean, when we want to find the value of the function at the position $x=1m$,...
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101 views

Why are we using Newton’s second law of motion to re-define the units of force? [closed]

Why are we using Newton’s second law of motion to re-define the units of force when we must already have units to measure the force? According to Newton’s second law: $$a\propto F \tag{1} $$ $$a\...
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Dimensional Analysis on Rotational Motion Laws

So I was solving some rotational motion problems when I decided to include the units in solving (just realized the necessity of doing this). Then I ran into some problem regarding the units in the ...
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Regarding the units of a proportionality constant

I got a general query regarding variation of two physical quantities. If we have two physical quantities say $A$ & $B$ such that $A$ is directly proportional to $B$. There exists a proportionally ...
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1answer
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How should units be treated?

First sorry I don't know how to properly use this page yet. Secondly, in a electricity problem I've found the following expression: $$(q_1*q_2)/r_1 +(q_1*q_3)/(r_1+r_2)+(q_2*q_3)/r_2=0\tag{1},$$ and ...
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1answer
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Derive the conversion factor from SI to Geometric units [closed]

In the geometrized system of units, $G = c = 1$. This directly gives us the definitions for second and kilogram in this system, as $1\:s = c_0\:m$ and $1\:kg = G_0c_0^{-2}\:m$, where I have used the ...
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Units in orbital modeling

I'm trying to make a simulation of simple planetary orbits in Python (with only Earth and Jupiter) and was wondering if there are any convenient units one could use? I currently have the gravitational ...
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What happens to radians in this calculation? [duplicate]

I rewrite N as kg m s^-2 and try to get Pmax, which is in Watts to kg m^2 s^-3 but when I do so I am left with an rad^2.
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Working with CGS units when calculating magnetic moment

I am attempting to calculate the total magnetic moment of a spherical object with known volume magnetic susceptibility $\chi$ in an $\mathbf{H}$ field of 1000 Oe. I need to do this in CGS units. Let'...
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80 views

How do you explain the unit of this formula?

I have trouble trying to interpret the following formula: $$G_{SCI} = \mu N^{span} G^3 \mathrm{arcsinh}\,(\rho \Delta f^2)$$ $$G_{SCI} = \frac{P_{SCI}}{B},$$ where $P_{SCI}$ is the self-channel ...
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Why $k$ is chosen to be unitless? [duplicate]

In $F = kma$, why $k$ is taken to be unitless? If $k$ is unitless and 1, then we have $F=ma$. This means (I guess) the physical quantity Force is product of different (from Force) physical quantities ...
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Is $\hbar, c, e$ truly independent? [closed]

Considering the constants: $\hbar, c, e$. Basically people considering them as very independent constant. However, if you think about it, $\hbar$ was initially introduced during $E=\hbar \nu$, thus ...
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In addition to $K_e/K_m = c^2$ (due to James Clerk Maxwell), are the constants that arise from $G/K_m$ and $G/K_e$ also limits?

Prior to James Clerk Maxwell we understood there to be three laws: $$\text{Gravity: }\;\;\; F_g= G \frac{m_1m_2}{r^2}\hat{r}$$ $$\text{Electricity: } F_e= K_e \frac{q_1q_2}{r^2}\hat{r}$$ $$\text{...
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Finding the difference of two temperatures of $^\circ \rm C$ in Kelvin

Denote by $a$ and $b$ temperatures measured in $^\circ \rm C$. My aim is to find their difference in Kelvin ($\rm K$). I thought of this question for fun after noticing that I can approach this ...
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Balance the units of the following hamiltonian

The following image is taken from an article and shows the hamiltonian of a spin chain model. I knew that the dimensional units in an equation must balance. To ensure this, the author took a procedure ...
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Why is current measured in coulombs per second and not in electron per second?

If electricity is produced by flow of electron, that is current, then current should be measured in electron per second, why is it measured in coulombs per second?
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Does parsecs times arcsec/yr equate to any specific unit?

Basically, I wanted to know if one multiplies proper motion (in arcsec/yr) to a distance (in parsecs), without conveting it to km/s (not multiplying it by 4.74, the conversion rate), does it equate to ...
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When is a parameter considered small for perturbation and how does physical units affect that?

In perturbation theory procedures (not specific to any particular topic) we tend to have (or delibrately insert) some small variable $\epsilon$ in an equation that is otherwise difficult to solve if ...
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Calculating errors based on other variables

I am trying to calculate the mass and respective error of a star in kg. I have the numbers in units of $M_{Sun}$,in the form $M_{star}=(a\pm b)$ $M_{Sun}$. Given that I have the mass (with error) of ...
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Units associated to PID Terms [closed]

I am trying to understand PID Controllers .. I don't understand very well what Physical Quantity is associated to each PID Term, The Block Diagram of PID is this: the PID Equation is this: $$ u(t)=...
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Is the equation $g=GM_Em/R_E^2$ in Tipler incorrect?

I was reading my textbook (Tipler et al.), and I am unsure of one of the expressions they used. On page 374, it says (near Figure 11-10) that $g = GM_Em/{R_E}^2$. Is this even dimensionally correct? ...
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When was magnetic field, first, mathematically defined?

The reason I'm asking this is, that we see that there is a constant $\mu$, in biot-Savart's law. If they were the first one to define it why did they use a constant? They could have simply left the ...
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Is this textbook answer incorrect? [closed]

In my physics textbook (Tipler et al.), the following equations were given as a solution to a problem. I am slightly in doubt of their equations. I think the answer should be $\frac{m_2}{m_1+m_2+(I/R^...
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1answer
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Gaussian (CGS) unit of temperature: is there a statkelvin?

In the Gaussian (CGS) system of units, the unit of electric charge (statcoulomb) is derived from the units of length, mass and time. Using Coulomb's law, we find that the dimension of electric charge ...
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Problem in $\sin\theta \approx \theta$ approximation [closed]

This approximation is used oftenly in physics: $$\sin\theta \approx \theta$$ This approximation is valid for small value of $\theta \leq10°$): But $\sin 1°=0.0174524064$ $\sin 2°=0.0348994967$ $\...
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Dimensionless expression for differential equation

I am working through Nonlinear Dynamics and Chaos by Steven H Strogatz. In chapter 3.5 (overdampened beads on a rotating hoop), a differential equation is converted into a dimensionless form. I am ...
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70 views

Anything having mass has an equivalent amount of energy

The Wikipedia article on Mass–energy equivalence (i.e. $E=mc^2$) states "anything having mass has an equivalent amount of energy and vice versa..." But how can we compare their amounts when the ...
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63 views

Metric elements of the Schwarzchild metric

I am learning about the Schwarzchild metric $g_{\mu\nu}(x)$ for the spacetime geometry outside a spherically symmetric source with mass $M$. In the book by Cheng, a spherical coordinate system $(t,...
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43 views

Unit Conversion with Temperature and Mixed Dimensionality

So, I understand the relationship between K(Kelvin), R(Rankine), C(Celsius), and F(Fahrenheit), and the complications of converting between them (i.e. varying meaning of zero). However, when ...

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