# Tag Info

1

Let's do natural units the other way around. Suppose that we've always worked with natural units, we measure time and distances in the same units and then some crazy physicist comes along who puts in factors of c in equations, e.g. $$ds^2 = dt^2 - dx^2 - dy^2 - dz^2 \longrightarrow c^2 dt^2 - dx^2 - dy^2 - dz^2$$ He then defines a meter and a second such ...

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The point of natural units is to rescale your units so that $c = 1$ and $\hbar = 1$ and $k_B = 1$. This is technically a type error because the quantities on both sides have different dimension, but it means "in the dimensions that give this the appropriate size." So this means that you have a $\text{cm time}$ unit, for example, which is the time it takes ...

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Simply multiply by $d/d$, where $d$ is a arbitrary distance, then the unit of $d/(hv)$ will be (Joule)^(-1), and $\frac{Z_1Z_2e^2}{d}$ will be in $J$. Then the product is dimensionless.

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I learned to keep track of the conversion from SI to Gaussian units for electromagnetism as \begin{align} \frac{e^2}{[4\pi\epsilon_0]} &= \alpha \hbar c \end{align} where the factor in [brackets] is unity in CGS units and isn't in SI. This is a nice way to remember things because it makes clear that Coulomb's law for two fundamental charges, $$\vec F = ... 4 You've been done a disservice if your earlier teachers didn't even mention the existence of Gaussian units (a cm-gram-sec system with "unrationalized" E&M). Not that I like them, but simply because they were very common in the mid twentieth century and they still have their adherents (some even on Physics SE). The unit of charge goes by several names ... 1 However, say we interpret that last number as ft * lb A kilowatt hour per rpm is not a foot-pound - you cannot "interpret" it as that.$$W=\tau\cdot\thetaP=\frac{W}{t}P=\frac{\tau\cdot\theta}{t}=\tau\cdot\omega, where $\omega$ is your angular frequency in rad/s (about 500 rad/s, in the case of 5000 RPM). Plug in 100 horsepower for your ...

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Just an accident. You've discovered that the ratio of $1\text{hp}$ to $1\text{kW}$ (0.7457) is pretty close to the ratio of a $\text{N m}$ to a $\text{ft lb}$ (0.7376). So if you apply one of them and the reciprocal of the other, the answer doesn't change much. As the value for horsepower isn't derived from other units (it's a measured quantity), there's ...

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In the SI system of measurement, one Newton of force accelerates a 1 kg mass at 1 m/s^2. This is very convenient, as there is no "factor" that you have to worry about when doing force, work, and energy calculations. In the U.S. customary units of measurement, the unit of force is the lbf, or pound-force. The unit of mass if the lbm or pound-mass. One lbf ...

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I'm unclear on exactly what you're asking, but most (all?) of the US customary units are ultimately defined in terms of SI units. As an example a US inch is defined to be exactly 2.54cm. Mass in US units is still just mass. The only real complication is the fact that the "pound" has historically been used both as a mass and as a force (where it is the ...

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