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I have a rather basic mathematical question regarding converting units. I have read some papers that measure a given variable in Joules per meter square (Jm^{-2}) and others that measure the variable in g*cm/cm . Is it possible to convert from one to the other?


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A Joule/m^2 is the same as kg/s^2, a g/cm has no relation to time. I doubt you can but some context would help. Is there an acceration mentioned? – kaine Jan 14 '13 at 20:53
up vote 1 down vote accepted

The units are not comparable: a joule is $1\dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^2}$, so $1\dfrac{\text{J}}{\text{m}^2}=1\dfrac{\text{kg}}{\text{s}^2}$ has units of $\dfrac{\text{mass}}{\text{time}^2}$, not $\dfrac{\text{mass}}{\text{length}}$, like $1\dfrac{\text{g}}{\text{cm}}$.

Added: After glancing at this paper and this paper, I suspect that if $S$ is the stability index as described in the second paper, which has units of mass over length, then some people prefer to use $gS$, where $g$ is the acceleration due to gravity; this does have units of mass over time squared and appears to have a nicer physical interpretation as work done by the wind per unit of surface area. Numerically the two differ by a constant factor, so either can serve as an index.

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ok so what about Joule per square meter or g*cm/cm. check out this link – KatyB Jan 14 '13 at 22:46
@Kate: I think that the second one should be simply g/cm. I did a little bit of digging and found a possible explanation, which I’ve added to my answer. – Brian M. Scott Jan 14 '13 at 23:11
Thank you very much. – KatyB Jan 14 '13 at 23:16
@Kate: You’re welcome. (That was certainly a different kind of question!) – Brian M. Scott Jan 14 '13 at 23:18

A Joule is $(kg\cdot m^2)/s^2$, so $J\cdot m^{-2}=kg/s^2$. These units don't match up with $g/cm$, so no, it is not possible to convert between them.

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please see amended question – KatyB Jan 14 '13 at 22:49

Generally this is not possible.

$J = \frac{kg m^2}{s^2}$

If we try to convert you units:

$\frac{J}{m^2} = \frac{kg}{s^2} = 1000 \frac{g}{s^2}$

Obviously, squared seconds are not the same as centimetre. But tell us what is the actual variable and maybe we can help. There are cases when some constants are involved. For example, energy is sometimes measured in $cm^{-1}$ and you can convert that to Joules if you multiply the number by Planck constant and the speed of light.

As kaine mentioned in the comment, there might be some charasteristic acceleration involved. If we divide $\frac{g}{s^2}$ by some charasteristic acceleration (for example, gravitational), we can obtain $\frac{g}{cm}$.

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please see amended question – KatyB Jan 14 '13 at 22:47

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