On 12/09/2019 12:27, Brian Reay wrote:
NY wrote:
"Tim Streater" wrote in message
.. .
In article , Brian Reay
wrote:

Certainly if you are analysing a problem and checking the dimensions (a
useful technique, not always taught these days although I made a point of
teaching it), indice notation is probably far easier to use.

I agree about the usefulness of dimensional analysis.

If I can't quite remember a formula, I use dimensional analysis. Is the
dimension that the formula produces different to the dimension of the answer
that I would expect? Am I adding together terms which are not the same
dimension? If so, check that I've remembered the formula correctly.

v^2 = u^2 + 2 as

m^2.s^-2 = m^2.s^-2 + m.s^-2 . m [ie m^s.s^-2]


So if I had brainfade and mis-remembered it as v^2 = u + 2as, I'd soon
realise that something was wrong.


Likewise with

s = ut + 1/2 at^2

m = m.s^-1 . s [ie m] + m.s^-2 . s^2 [ie m]



Those are good examples.

Dimensional analysis used to be included in Physics, Im not sure if it was
at O or A level, it is sometimes difficult to recall when you learned
something you seem to have €˜always known. Speaking to a colleague when I
was still teaching, it was included superficially in Physics (I think A
level but possibly GCSE) but he was delighted when he learned I taught it
in my classes.

I find just being able to think in terms of dimensions - even if not
doing an accurate analysis on paper, it a very useful tool to catch
errors, and would also stop lots of silly mistakes.

Like how many times you see people talk about kW when they mean kWh or
vice versa. Just a basic understanding that the unit of energy is the
Joule, and that power in Watts is a measure of the rate of flow of
energy. Hence 1 Watt equates to one J/sec. Or energy over time. If you
then multiply by time, the two times dimensions cancel out and you are
left with just energy.


--
Cheers,

John.

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