# 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.).