Kg x kg

1. Sep 23, 2011

labview1958

Is there any quantity in physics that has the unit kg^2 in it?

2. Sep 23, 2011

chrisbaird

Nothing fundamental exists to my knowledge with those units. You could construct anything you want though. For instance, the Newtonian gravitational force between two bodies of identical mass is F = G r-2 m2. You could rearrange this to be m2 = Fr2/G and both sides now have units of kg2

3. Sep 23, 2011

Staff: Mentor

Take any physical quantity with units of kg and square it and give it a name. Then you have a physical quantity with units of kg^2.

I don't think that is what you mean, but I don't know what you really want.

4. Sep 24, 2011

Redbelly98

Staff Emeritus
I'm not aware of any useful quantity with units of kg2

5. Sep 24, 2011

Andy Resnick

That's an interesting observation: length and time both occur with many different exponents, but mass does not, apparently.

6. Sep 24, 2011

AlephZero

I'm not sure that exponents of length and time are completlely analogous though.

At least in classical physics, there seems (to me) to be a philosophical difference between an integral over an area or volume, leading to units of L2 or L3, and a double integration or differentiaton wrt time, leading to T2.

To give a specific example, for acceleration necessarily seems to need to be interpreted as (m/s)/s, but it doesn't make much sense to interpret density as ((kg/m)/m)/m.

One might say that space is intrinsically multi-dimensional, but time and mass are not.

And how the "MLT" units for electrical quantites, for example charge = M0.5L1.5T-1, relate to all this is another question!

7. Sep 24, 2011

lugita15

Could you elaborate on this?

8. Sep 25, 2011

Redbelly98

Staff Emeritus
There is an alternative system of units for electromagnetism, http://en.wikipedia.org/wiki/Gaussian_units" [Broken], where Coulomb's law is written without any proportionality constant:
$$F = \frac{Q_1 Q_2}{r^2} \text{ ,}$$
i.e. without the factor of k or 1/4πεo. With units of force and distance already defined in mechanical physics, this equation determines the units of charge in much the same way that F=ma sets the units of force to be MLT -2.

Solving the above equation for the charges, we get
$$Q_1 Q_2 = F \ r^2$$
So the units of charge2 are equivalent to F·r 2. Or we can say that the units of charge are equivalent to (F·r 2)1/2:
Charge units ~ (MLT -2 · L2)1/2 = (ML3T -2)1/2 = M1/2L3/2T -1

Last edited by a moderator: May 5, 2017
9. Sep 25, 2011

lugita15

Yes, I already knew about CGS units. I thought you meant there was a way to relate them in SI.

Last edited by a moderator: May 5, 2017
10. Sep 25, 2011

Andy Resnick

That's correct- notions of MLT are totally different than x-y-z (or variations thereof: xyzt, MLTQ, etc.).