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A major point of confusion in the NMR field is that of the dimensionless and hidden radian unit. This often results in people mistakenly writing Hertz units when inverse seconds (or rad/s) should have been used. This issue can be traced back to the [http://en.wikipedia.org/wiki/International_System_of_Units SI] organisation itself. Specifically the SI supplementary units definitions whereby the assumption is made that if a process is rotational, a physicist should know that radian units are implicit.
== Introduction ==
The concept of the hidden radian unit is quite important for understanding relaxation in NMR or, in fact, any rotational process in physics. For example it is important for understanding the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion. In these cases, the reason is because relaxation rates are measured in rad/s. As described in [[#SI supplementary units]], the radian unit can be dropped because it is plainly obvious that NMR and relaxation is an angular process and hence radian units are implied (if you didn't get that, that was sarcasm). Hence R2 can be said to be in units of 1/s, but never, ever Hz. Also note that because of the SI conventions described below, describing the correlation time in s units does not imply that there are no radian units. But reporting rates as Hz implies no radian units whereas reporting as 1/s instead indicates that radian units are present.
</math>
where <math alt="theta''θ(t)">\theta(t)</math> '' and <math alt="phi''ϕ(t)">\phi(t)</math> '' are the time dependent spherical angles in the dimensionless radian units. The time ''t '' is normal time and hence has no hidden radian units. Spherical harmonics are the angular portion of the solution to Laplace's equation and, because it is angular, it is using the radian angular SI unit.
== Rotational correlation times ==
[[Category:Theory]]