Yes I understand what it means: m.s^-2 or kg.m^-3 are identical to m/s^2 or kg/m^3. All I was saying is that the former is a slightly cack-handed way of expressing it (IMHO) and one which has to be translated back again if you are going to refer to it in spoken form. But it does make it easier to check that powers of units match throughout an equation.
Those are good examples.
Dimensional analysis used to be included in Physics, I?m 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.
It goes hand-in-hand with checking that the answer you get is *roughly* what you'd expect. If you calculate the volume of a hot-water cylinder and you get an answer of a couple of millilitres (a thimbleful) or a million litres (a swimming pool) then you've probably made a mistake ;-)
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.
I'm pretty sure we covered it in O-Level Physics.
SteveW
its to do with the fact that mathematically speaking:
1 / x is equivalent to x^-1So therefore
1/x^2 is equivalent to x^-2.so once the 1 is replaced by another quantity we have:
for density say:
kg / m^3 is equivalent to kgm^-3
but for what they are talking about it rarely matters to average users. What does the Kwh mean on fride/freezer consumption. such as 124Kwh
note that oa.com uses an uppercase K argos use kWh/year lower case K updercase W
When buying a kettle I found the figure of 3kw more useful than the fridge version and more useful than 10.8 mega joules of energy.
calories is an even more weird one.
a drink I have here per 100ml is 6kJ or 1 Kcal an average adult 8400 kJ or 2000 kcal
Is that 2000 calories or 2000 kilo calories which is 2 mega calories :-)
I'm left knackered ;-)
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