Removing Infinitesimal Mass Elements from a Hollow Sphere

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SUMMARY

The discussion focuses on the mathematical approach to removing the infinitesimal mass element (dm) when deriving properties related to a hollow sphere. The key point is that the differential mass depends on the object's density, which can be expressed in units such as g/cm³ or kg/m³. For a hollow sphere, the mass varies with the area, leading to a relationship with the differential radius (dr). The integration of dm for a spherical shell is highlighted as a necessary step in solving the problem.

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  • Understanding of differential calculus
  • Familiarity with concepts of mass density (g/cm³, kg/m³)
  • Knowledge of geometric properties of spheres
  • Basic integration techniques, particularly for spherical coordinates
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PSOA
How do I get rid of infinitesimal mass element dm?
 
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PSOA said:
How do I get rid of infinitesimal mass element dm?

I assume you're trying to derive the moment of inertia of a hollow sphere, but you should really be more specific when posting questions.
 
I am not determining the moment of inertia. I didn't specify what I was doing because I just wish to know of to solve this particularly problem. How to get rid of dm?
 
Your differential mass is the rate of change in the mass. It will depend on the object's density (g/cm^3, kg/m^3, etc).

In your case, you have a hollow sphere, so the mass will change in relation to the area (assuming the sphere has an infinitely small thickness). That would be g/cm^2, kg/m^2, etc.

That should allow you to change your variable to dr, the differential radius, since the volume and/or the area will depend upon the radius.
 
But I need the constant sigma M/A (equivalent to density) which I do not know.
 
Maybe Integrate? I don't really understand your problem.
 
I need to \int dm for a spherical shell.
 
PSOA said:
I need to \int dm for a spherical shell.

Look at the thread that started this.
 
Last edited:

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