On 12/09/2019 09:53, Robin wrote:
On 12/09/2019 09:00, Tim Streater wrote:
In article , NY wrote:

"Tim Streater" wrote in message
.. .
In article ,
David Paste wrote:

Hello,

When writing, for example, "metres per second per second" for
acceleration, it is noted as ms^-2 (where the caret symbolises
the -2 is in superscript).

I understand that, and why, "per second per second" is "seconds
squared", but in the notation, why is it superscript minus 2? Why
not just superscript 2?

Because its "per", and so you are dividing. which gives you a negative
coefficient.

E.g.:

Miles/hour is speed, and if I say I go at a certain miles/hour for a
certain time, the answer must be miles. So, 30 miles/hour for two hours
is 60 miles. That is:

30 m/h x 2 h = 60 m

So the /h and the h cancel, meaning that as the h is really h^1, the /h
must be h^-1 in order for the coefficients to add up to zero (meaning
there's no h left in the final expression). When you multiply things
you add their coefficients, as in 10^2 x 10^3 - 10^5.

The notation m s^-2 and kg m^-3 always strike me as perverse: what
was wrong with m/s^2 and kg/m^3? I remember being taught m/s^2, and
then when I changed school to one that did a Nuffield physics
syllabus, the notation changed to kg m^-2 which it claimed to be
"better" in some unspecified way.

I'm inclined to agree.


I disagree.Â* Mainly as the superscripts reduce the risk of mistakes
where there are multiple terms.Â* Eg

Â*Â*Â*Â*kg.m^ˆ’1.s^ˆ’2
Â*Â*Â*Â*kg/m.s^2

My understanding is that this is why the "simpler" notation is
deprecated. Also it is better when you are typing stuff from scratch. In
the old old days where manuscripts were hand-written and subsequently
transcribed by typists, or you were exchanging hand written calculation
sheets with colleagues the slash notation is slightly easier to read.
Especially if you express the formula as a fraction, with a full
horizontal line.