Linked Questions

1 vote
1 answer
520 views

How do the radian have a unit? [duplicate]

The radian is defined as the ratio of the circumference and the radius. Both are measured in meters. So there should not be a unit for that. But we use 'rad' as the unit of the radian value. The ...
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1 vote
4 answers
145 views

How do you interpret the radian in physics? [duplicate]

When calculating $\sin x$, $x$ needs to be radian to calculate it. so for example when solving Uniform Circular motion, $x(t)$, $y(t)$ can be expressed $$x(t)=R\cos(ωt) [m] $$ $$y(t)=R\sin(ωt) [m]$$ ...
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  • 11
0 votes
3 answers
166 views

Degrees vs radians [duplicate]

I’ve been messed over on a test (at least one that I can clearly remember, probably at least a few more) (and it was only a few points, but still very frustrating) because I forgot to switch my ...
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0 votes
0 answers
29 views

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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  • 47
73 votes
9 answers
19k views

Why are "degrees" and "bytes" not considered base units?

From Wikipedia: The SI base units and their physical quantities are the metre for measurement of length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for ...
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50 votes
6 answers
10k views

Why can fuel economy be measured in square meters? [closed]

With help from XKCD, which says Miles are units of length, and gallons are volume — which is $\text{length}^3$. So $\text{gallons}/\text{mile}$ is $\frac{\text{length}^3}{\text{length}}$. That's ...
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  • 569
29 votes
12 answers
16k views

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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  • 353
16 votes
7 answers
6k views

Why are radians more natural than any other angle unit?

I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
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3 votes
2 answers
5k views

What are the reasons for making the mole a base SI unit? [duplicate]

We have meter in the SI - we use that to measure length. Other length units like light years can be expressed in meters. But how often do we express amounts or quantities in moles? Mole is a number of ...
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  • 3,038
7 votes
1 answer
2k views

Why revolutions (or turns) are dimensionless?

I think that the reason is because one revolution or one turn is equal to $2 \pi$ rad or to $360$ degrees. We can relate rads and degrees to two units of length that cancel each other. rad $= \frac{...
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  • 71
0 votes
2 answers
2k views

Is the Weber-Turn a real unit?

We have been studying electromagnetic induction in Physics and when calculating Flux Linkage our teacher insisted the unit is Weber-Turns since it is the flux times the number of turns. I put forward ...
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1 vote
2 answers
205 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). ...
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2 votes
2 answers
140 views

What are the units of wavenumber? With or without radians?

Sometimes, I see that wavenumber units are $\text{m}^{-1}$, but on the other hand, (and by definition of $k = \omega/v = 2\pi/\lambda$), it is $\text{rad/m}$. What is correct?
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0 votes
1 answer
122 views

Units of angular frequency in a simple harmonic oscillator [closed]

The equation of a simple harmonic motion can be $x=A \cos(\omega t)$. $\omega$ therefore has units of $radians/sec$. I was solving some problems when I found a statement on my notes $x=\left(1+\...
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  • 718
0 votes
2 answers
61 views

Unit of angular velocity in oscillatory motion

Suppose an angular oscillatory motion. In the function below, $\alpha$ and $\alpha_o$ are angles measured in radian, $\omega$ is circular frequency ($2\pi/T$) measured in [radian/s] and $t$ is time. $$...
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