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

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Specific Heat of tissues vs kcal (Weird Thermodynamics question)

I'm a YouTuber who over-examines video game physics for the purposes of both education and entertainment, and I've run into a bit of a snag while researching my next video. I'm looking into heating ...
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1answer
43 views

Is this differential equation (for damped & driven physical pendulum) physically valid?

Following is the equation of motion for a physical pendulum which is damped and driven by a force of frequency $f$: $$\frac{d^2 \theta}{dt^2} + b \frac{d\theta}{dt} + sin(\theta) = Tsin(2\pi ft)$$ ...
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0answers
24 views

Defining Thermodynamic beta in unit of second

If I define Thermodynamic beta in unit of second. Does this mean that: Boltzmann constant $k$ is unit-less? $T$ is in units of frequency (Hz) or Kelvin $K$? In this case, is defining Thermodynamic ...
-1
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0answers
43 views

What is the significance of the so called Planck force? [duplicate]

So, what is the significance of the so called Planck force, and why is it called Planck force, when it has nothing to do with any of the Planck's discoveries? The Maxwell’s wave equation is $\nabla^...
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1answer
34 views

What are dimensions of co-ordinates which are used to define an electric field?

A possible electrostatic field is: $ E_x = 6xy$ $ E_y = 3x^2-3y^2$ $ E_z = 0$ Suppose we are using SI system. So unit for components of field is volts/meter. Then what are dimensions of $x$ and $...
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1answer
34 views

How to treat the units of measure when taking a derivative?

I've had a doubt for a long time: when I'm taking the derivative, of a function for example, how should I treat the units of measurement? For example, if I'm taking the derivative of: $$S\,[{\rm m}]=...
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1answer
49 views

Why does $k^z/E$ have dimensions of inverse velocity rather than velocity?

I'm studying quantum field theory and I want to prove the cross section. In Peskin's book, equation 4.77 says that: $$ \frac{1}{\left | \frac{k_{A}^{z}}{E_{A}}-\frac{k_{B}^{z}}{E_{B}}\right |}=\frac{...
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4answers
587 views

Are quantum operators dimensionless?

I'm slightly confused as to whether quantum (hermitian) operators, which we get by promoting observables to operators, are dimensionless or not? Clearly the Hamiltonian of the system, say of the ...
4
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2answers
580 views

Check dimensions of the integral of a function

I and a colleague are arguing about the dimensions of: $$\int_0^x f(x) dx $$ in this particular case $[f(x)]=m^2/s^3$ and $[x]=m$. Does it follow that $[\int_0^x f(x) dx]=m^2/s^3$ or $[\int_0^x f(x)...
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1answer
24 views

how sound quantity in a period of time is measured by? [closed]

Let's suppose that I'm singing for 10 minutes and I obviusly produce some sounds, and let's imagine that I hold an instrument for measuring the amount of sounds produced within that period of time. I'...
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2answers
50 views

What does J cm-1 stand?

For an optical component, I got following number as an optical damage threshold from the company, damage threshold = 10 Jcm-1,20ns, 20Hz It looks like 20ns is ...
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2answers
41 views

Where is the periodic nature in the Cs atomic clock? [closed]

In case of pendulum clock,lets say one swing ticks one second..but what is the analogy in case of CAESIUM atomic clock? Is 9,192,631,770 ticks is equivalent to one tick in pendulum clock? And how we ...
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0answers
25 views

Why is metre defined in terms of distance covered by light in 1 second? [duplicate]

Why is the unit of length defined with the help of unit of time? (1m=x covered by time in 1/3*10^8 s) Isn't length a fundamental unit too, why is it defined in terms of an other unit?
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1answer
30 views

What would be the standard for the unit of pressure Pa or MPa?

Me and my friend are doing a project and in our result we shall provide a plot, and on our axes we are going to write out the units. My friend wrote "xx MPa", claiming it was standard in reports to ...
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2answers
89 views

What is the dimensional formula of angular velocity?

I have problem to determine the dimensional formula of angular velocity. My friend said that the dimensional formula of angular velocity is $T^{-1}$. It's come from rad/s, rad is dimensionless, the ...
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1answer
30 views

Differences in notation of momentum 4 vector

I have noticed three ways to write the 4 momentum vectors: $P = (E/c, \vec{p})$ $P = (E, \vec{p})$ $P = (E, c\vec{p})$ I know how to derive equation 1, and as far as I know, one can use the ...
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0answers
42 views

Photon Propagator in QFT

Please forgive my temporary split-brain, but I'm a little thrown off by something when considering units at the moment. In QED (depending on the guage), the photon propogator is written as $<0|\...
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1answer
78 views

When can the constant of proportionality in an eq be set equal to 1 and when not? [duplicate]

In $F=kma$, $k=1$ but in $F=kx$, $k$ is not equal to 1?So what are the conditions for the constant of proportionality to be set 1?
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1answer
35 views

In this energy conservation problem, why are the answers different with different units? [closed]

Really basic question, but basically I'm given a change in height in centimeters (that's how I measured it). From that, I'm supposed to find the initial kinetic energy. $KE_i = PE_f$ After doing ...
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3answers
78 views

How do Calories (kcal) relate to watts?

In thinking about exercise and "burning calories" it occurred to me that there should be some fairly intuitive correlation between the biological energy conversion going on in a person's body with the ...
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2answers
60 views

Proper units for physical quantities when $\hbar$=$1$

How to deal with the units of quantities if $\hbar=\tfrac{h}{2\pi}=1$? For example, the energy $E=\hbar\omega$: If I have chosen $\hbar=1$, how do I use the units to properly differentiate between ...
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6answers
65 views

The Kelvin-Celsius problem

Let's suppose we have temperatures 30°C and 35°C. Converting them to Kelvin we have 303.15K and 308.15K. In the second case, the temperature difference is 5K. While in first case, temperature ...
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1answer
41 views

Is there a software to convert units for quantities and equations? [closed]

For example, Often I end up with a complicated equation that uses non-standard units. In these equations, Temperature is in eV and Magnetic field is in Gauss. I need to convert my equation to another ...
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0answers
40 views

Is there a 3D analogue of angle?

A one-dimensional angle is a wedge, almost like a slice of pizza. A two-dimensional angle is an angle squared, like the cone of light produced by a flashlight. This is called a solid angle. Is ...
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1answer
101 views

Is meters per second equivalent to seconds per meter?

I know this question is probably ridiculous, but bear with me for a moment. This thought emerged while I was converting between nm and wave numbers ($\rm cm^{-1}$). In order to prove this conversion, ...
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1answer
47 views

Fine structure constant and unit conversion [closed]

In a paper I'm reading, the author writes down the following formula: $$\Gamma=\dfrac{\alpha^2}{576\pi^3}\dfrac{\left(4+z\right)^2}{z}\dfrac{m^5}{m^2_\pi f_\pi^2}$$ $\Gamma$ is a function of $m$ (in ...
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1answer
36 views

What are the units pm/K?

I can only think of picometres, but it doesn't seem to make sense. Here is the context, from the paper 'Towards Reproducible Ring Resonator Based Temperature Sensors', Klimov et al., Sensors & ...
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0answers
22 views

Arguing on dimensions of logarithms and exponentials [duplicate]

Suppose you have some physical quantity $x$ of dimension $l$. We all know that the dimension of $x^2$, for example, will be $l^2$, and that of $\dfrac{1}{x}$ is $l^{-1}$. However, what will be the ...
117
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13answers
10k views

Are units of angle really dimensionless?

I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've ...
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12answers
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Do all equations have identical units on the left- and right-hand sides?

Do all equations have $$\text{left hand side unit} = \text{right hand side unit}$$ for example, $$\text{velocity (m/s)} = \text{distance (m) / time (s)},$$ or is there an equation that has different ...
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2answers
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how do we actually count the number of magnetic field lines and what does the gap between those lines describe?

on the internet,(http://nuclearpowertraining.tpub.com/h1011v1/css/h1011v1_53.htm), there is a statment which says that 1 Wb is $1\times 10^{8}$ magnetic field lines. My question is, How do we count ...
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1answer
147 views

Difference between theoretical equations and empirical equations

Some equations are theoretical in the sense that they are derived from an underlying theory. Other equations are empirical in the sense that they were selected only because they fit experimental data ...
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2answers
36 views

Why does the angular speed formula end up in radians per second?

So, in my homework I am given the radius and also the tangential speed $v$, the measurement for radius is meters; the measurement for $v$ is $m/s$. I don't understand how by after calculating the RPM ...
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3answers
445 views

Why do we need constants? [closed]

This question is driving me crazy because I cannot find a straightforward answer. I want to know what a physical constant exactly is. I know that it’s a value that doesn’t change, but what is it? Why ...
3
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1answer
47 views

How to read this length interval in imperial units?

I am from Europe and I do some research for my thesis. I found this picture, which is very usefull for me, but unfortunately the lengths are in imperial units (for lenght they are using something like ...
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1answer
36 views

Classification of plane angle as fundamental or derived

I recently started with my high school studies and the chapter I am stuck at is units and measurements. I was told about two types of physical quantities and my teacher gave me the following ...
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3answers
165 views

Why did Einstein took speed of light unit or constant in his equation of relativity?

We can find that no object can have speed more than light from Einstein's equation of relativity because if anything have speed more than light then we get -ve value within square root. But why did ...
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1answer
125 views

What is the difference between emu and esu?

Ok...so this is the statement given in my book: a) In C.G.S System the unit of charge is electrostatic unit of charge (E.S.U). It is also called Stat Coulomb (StatC). b) In C.G.S system, the unit ...
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50 views

What kind of unit is $m^2s^{-4}$ in terms of gyro/accel?

Background While working on something in the field of avionics, I have discovered the following unit as part of an inertial-physics equation... $$m^2s^{-4}$$ I am trying to figure out the formal ...
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1answer
25 views

why this formula has answer in micrometer

Formula e=0.8+0.06(m+0.25√d) e=pitch error in microns m=module in mm d= pitch circle diameter in mm From school we have learned that if we put value of terms like m and d (terms from above example) ...
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9answers
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How to interpret the units of the dot or cross product of two vectors?

Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters. If I take their dot product with the algebraic definition, I get this: $$a \cdot b = 1\mathrm m \cdot 4\...
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5answers
1k views

Units don't match in the torsional spring energy!

According to Wikipedia's description of torsion springs and according to my understanding of physics the energy of a torsional spring can be written as $$U=\frac{1}{2}k \varphi^2$$ where $k$ is a ...
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1answer
66 views

Does the imperial system have any advantages (besides its wide acceptance in the US)? [closed]

The United States (and one other country, somewhere in Africa I think) uses the imperial system (feet, pounds, etc.), while pretty much everyone else uses the metric system (meters, kilograms). The ...
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2answers
47 views

Definition of atmosphere unit and relation to temperature and gravity

I've seem sometimes the atmosphere unit for pressure be defined so that $1\ \mathrm{atm}$ would be the mean atmospheric pressure at sea level. I've seem on the other hand the following definition: ...
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1answer
64 views

Which was the first Coulomb's constant value? [closed]

Which was the first Coulomb's constant value? I didn't found any info in the Internet. I need the first value of K to compare it with my experiment. Could you please help me?
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3answers
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What does the $k_e$ in Coulomb's law and $G$ in Newton's Universal Gravitation Law mean?

I very well understand the proportionality relation that was used to derive these laws like $F$ is proportional to product of masses and inversely to radius squared and hence its proportional to the ...
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1answer
30 views

What is “unity constant form” and why is it useful?

I read the following in a tutorial: The standard transfer function of a first order system is: $$G(s) = \frac{k}{s + a}$$ Arranging this into unity constant form gives: $$G(s) = \...
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2answers
155 views

Dimensions of physical quantities in quantum mechanics

In most introductory quantum mechanics classes, we are introduced to the Dirac notation, concept of the 'state' of the system being represented as an abstract vector in the Hilbert space associated ...
2
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3answers
111 views

How can geometrized units have more than one constant equal to 1?

I can understand how you could manipulate units to make a certain constant equal to $1$, like $c$ or $G$, et cetera. But how can you make it so two constants (in this case $c$ and $G$) are equal to $1$...
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2answers
74 views

About unit definition in numerical computation [closed]

I attend an undergraduate level course of quantum mechanics. I am thinking of computer computation on a quantum mechanical problem. I do not have much experience in numerical computation, so I read ...