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

[labview1958]

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

 

[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

 

[Dale]

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

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.

 

[Redbelly98]

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

 

[Andy Resnick]

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

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

 

[AlephZero]

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

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 = M^0.5L^1.5T^-1, relate to all this is another question!

 

[lugita15]

And how the "MLT" units for electrical quantites, for example charge = M^0.5L^1.5T^-1, relate to all this is another question!

Could you elaborate on this?

 

[Redbelly98]

And how the "MLT" units for electrical quantites, for example charge = M^0.5L^1.5T^-1, relate to all this is another question!

Could you elaborate on this?

There is an alternative system of units for electromagnetism, http://en.wikipedia.org/wiki/Gaussian_units" , 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 1/4πε_o. 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 = M^1/2L^3/2T ^-1
​

 

[lugita15]

There is an alternative system of units for electromagnetism, http://en.wikipedia.org/wiki/Gaussian_units" , 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 1/4πε_o. 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 = M^1/2L^3/2T ^-1
​

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

 

[Andy Resnick]

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

<snip>

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