Re: [Phys-L] form of Newtons 2nd law

[John Denker <jsd@av8n.com>]

On 07/26/2012 10:19 PM, John Mallinckrodt wrote:
> Silly, but no sillier than equations like f = 2*pi*omega.  Frequency is frequency.

I agree with the sentiment.  Frequency is frequency.

  Minor nitpick:  Writing f = 2*pi*omega is probably even sillier than was intended.
  The more common everyday silliness is the other way around:  omega = 2*pi*f.

To make a constructive suggestion out of this, consider the following scenario:
Suppose you are doing Fourier transforms.  The usual choice is to write factors
of either
      exp(i ω t)        [1]
or 
      exp(2 π i f t)    [2] (allegedly)

However, taking to heart JM's advice, the latter really should be written as

            2 π
      exp(-------- i f t)   [3]
           Hz sec

which makes [3] the same as [1] in all ways, formally, practically, and otherwise.
In particular, if we consider the example of

           f = 100 Hertz
           ω = 314 inverse seconds

we see that frequency is frequency, and ω equals f ... provided you take the units
into account.  The factor of 2π in equation [2] is a mistake.  The units are wrong.
I personally have made this mistake more than once, but I now repent.

                2 π
The factor of -------- is a classic "factor-label" factor.  It is a factor of unity.
               Hz sec