I know that $\hbar$ is $h / 2\pi$ - and that $h$ is the Planck Constant ($6.62606957 × 10^{-34}\:\rm J\:s$). But why don't we just use $h$ - is it that $\hbar$ is used in angular momentum calculations?
Answer
Perhaps some additional information is in order to shed additional light...
The whole discussion begs the question: If $\hbar$ is so convenient, why do we have $h$ around?
As usual, "historical reasons".
Planck originally invented $h$ as a proportionality constant. The problem he was solving was blackbody radiation, for which the experimental data came from spectroscopy people. And spectroscopy people used $\nu$ (for frequency, for that or wavelengths were what they measured). So the data was tabulated in frequency. So, when he formulated his postulate, he used $E = nh\nu$ for his quantization.
In modern theory, we prefer working with $\omega$ rather than $\nu$, because it is annoying to write $\sin (2\pi\nu t)$ rather that $\sin (\omega t)$. With angular frequencies, the quantization postulate becomes:
$E = n \frac{h}{2 \pi} \omega$
Now life sucks. So we invented the shorthand:
$E = n \hbar \omega$
We are happy (almost) everywhere. If Planck had spectroscopy data in $\omega$, we probably would not have a bar on the $h$ now...
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