Standardised versions of these units can also help us in physics.
We can derive pretty well all of classical physics from a few basic units, called dimensions.
Mass - M
Length - L
Time -T
Temperature - $\displaystyle \theta $(greek theta)
Current - I
This can for instance tell us if we have an equation correct or compare quantities
so kinetic energy = $\displaystyle \frac{1}{2}m{v^2}$
$\displaystyle KE = \frac{1}{2}m{v^2} = \frac{1}{2}M{\left( {\frac{{dis\tan ce}}{{Time}}} \right)^2} = M{L^2}{T^{ - 2}}$
and potential energy = mgh or
$\displaystyle PE = mgh = M\left( {\frac{{velocity}}{{Time}}} \right)L = M\frac{{\frac{{dis\tan ce}}{{time}}}}{{time}}L = M{L^2}{T^{ - 2}}$
and we can see that both have the same dimensions (so long as we work in the same units) - and these are the dimensions of energy.
Note we do not include the dimemsions of the half in the kinetic energy because it is just a number, but some constant have dimensions, as with the aceleration due to gravity in the potential energy formula and these must be included.
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Last edited by studiot; Apr 30th 2017 at 12:42 PM.
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