Convert linear density to area and volumetric density?

AI Thread Summary
To convert area density to linear and volumetric density, the shape of the object is crucial; in this case, it is a flat square surface. The total mass can be calculated using the formula M = σA, where σ is the area density and A is the area. The volumetric density is derived as ρ = σ/T, with T representing the thickness of the plate. Linear density is only constant along the direction parallel to one side of the plate. Understanding these relationships allows for accurate conversions between different density types.
silverdiesel
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if I am given a area density of 10^-4, I can get linear and volumetric density from that right? I just can't seem to figure it out.
 
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silverdiesel said:
if I am given a area density of 10^-4, I can get linear and volumetric density from that right? I just can't seem to figure it out.
Only if you know the shape of an object you are working on.
 
It is a square (not a cube, a flat square surface)
 
silverdiesel said:
It is a square (not a cube, a flat square surface)
Then the total mass of the object is

M = σA

The volume density is

ρ = M/V = σA/V = σA/(AT) = σ/T

where T is the thickness of the plate.

If you want the linear density, it is only constant in a direction parallel to one side of the plate. See if you can do that one.
 

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