11–20 of 26 posts
> This means that, if you follow the rules of the SI, 1 Hz = 1/s = 1 radian/s I fail to see how this follows from the SI definition of either the hertz or the radian.
// Alan's notes:
// I'd like to put a mu in here for micro.
// Should we adopt the questionable Electrical Engineer policy of using
// "u" to indicate micro? I've added "uF" for microfarad later on to
// tackle the most common case.
Disclosure: Graduate of EE. Didn't know we were causing so many issues all this time with our rebellious use of microfarads :)
> This means that, if you follow the rules of the SI, 1 Hz = 1/s = 1 radian/s I fail to see how this follows from the SI definition of either the hertz or the radian.
I always frowned upon the unit "radian". Radian is defined in terms of the ratio of two quantities both having length dimensions. So by this definition angle should be dimensionless. I really don't get radian.
EDIT: [0] For example, one way of defining sin(x) is as the sum of the power series `x - x^3/6 + x^5/120 - …`; this cannot be dimensionally consistent unless x is dimensionless. Another is to define y(x) = sin(x) to be the solution of `d^2y/dx^2 = -y` satisfying certain initial conditions; but the units of `y` can only be equal to those of its second derivative if the argument of `y` is dimensionless.
EDIT 2: One easy way to fix the potential dimensional inconsistency is to replace `d^2y/dx^2 = -y` by `d^2y/dx^2 = -k^2 y`, where `k` is just a conversion factor for dimensional consistency (so that `[k] = [x]^{-1}`). Then a solution is `y = sin(k x)`; and, once again, the argument of the sine function is dimensionless.
> This means that, if you follow the rules of the SI, 1 Hz = 1/s = 1 radian/s I fail to see how this follows from the SI definition of either the hertz or the radian.
> I fail to see how this follows from the SI definition of either the hertz or the radian.
The definition of 'Hertz' is 1/s. 'Radian' is not a unit, but a dimensionless number (the number 1, in fact, representing the ratio of arclength to radius where the arclength and radius happen to be the same), so that 1/s = radian/s.
In regards to the difference between American and European billion/trillion/etc: // These number terms were described by N. Chuquet and De la Roche in the 16th // century as being successive powers of a million. These definitions are // still used in most European countries. The current US definitions for these // numbers arose in the 17th century and don't make nearly as much sense. Huh? Admittedly I'm biased, being…
I think the "making sense" refers to the fact that "billion" has "bi-" as a prefix, and "trillion" has "tri-" as a prefix. In American English, it's not clear what is "bi-", exactly, about a billion -- two of what? If we had skipped "billion" and gone with "trillion" = 1e9, then it would be more natural, because then it would refer to the number of thousands; but then the more natural nomenclature would be "bi-sands"…
Just in case anyone is confused by this: (maybe it's just me?) // Alan's notes: // I'd like to put a mu in here for micro. // Should we adopt the questionable Electrical Engineer policy of using // "u" to indicate micro? I've added "uF" for microfarad later on to // tackle the most common case. This is referring to using the practice of using the character "u" instead of "µ" as the SI prefix for micro-, presumably be…
Also, the ohm symbol is frequently omitted from resistance specifications. 10 kΩ is written as 10 k (or worse, 10k).
> This means that, if you follow the rules of the SI, 1 Hz = 1/s = 1 radian/s I fail to see how this follows from the SI definition of either the hertz or the radian.
I always frowned upon the unit "radian". Radian is defined in terms of the ratio of two quantities both having length dimensions. So by this definition angle should be dimensionless. I really don't get radian.
> This means that, if you follow the rules of the SI, 1 Hz = 1/s = 1 radian/s I fail to see how this follows from the SI definition of either the hertz or the radian.
> > This means that, if you follow the rules of the SI, 1 Hz = 1/s = 1 radian/s > I fail to see how this follows from the SI definition of either the hertz or the radian. The definition of 'Hertz' is 1/s. 'Radian' is not a unit, but a dimensionless number (the number 1, in fact, representing the ratio of arclength to radius where the arclength and radius happen to be the same), so that 1/s = radian/s.