# Removing Infinitesimal Mass Elements from a Hollow Sphere

• PSOA
In summary, to get rid of the infinitesimal mass element dm for a spherical shell, you will need to integrate it with respect to the radius using the formula for density, which will depend on the object's dimensions (g/cm^3, kg/m^3, etc). This will allow you to change your variable to dr, the differential radius, and solve for your desired result.
PSOA
How do I get rid of infinitesimal mass element dm?

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:

## What is a hollow sphere?

A hollow sphere is a three-dimensional shape that is completely empty on the inside, with only a thin outer shell. It is typically in the shape of a ball and is often used in engineering and scientific applications.

## What are infinitesimal mass elements?

Infinitesimal mass elements are extremely small particles that have a negligible mass. They are often used in mathematical models to represent the behavior of a continuous object or system.

## Why would one want to remove infinitesimal mass elements from a hollow sphere?

Removing infinitesimal mass elements from a hollow sphere is often done in mathematical models to simplify the calculations and make them more manageable. It can also help to better understand the behavior of the sphere in certain scenarios.

## What is the process for removing infinitesimal mass elements from a hollow sphere?

The process for removing infinitesimal mass elements from a hollow sphere involves taking the limit as the size of the mass elements approaches zero. This can be done using mathematical techniques such as integration or differential equations.

## What are the potential impacts of removing infinitesimal mass elements from a hollow sphere?

The impact of removing infinitesimal mass elements from a hollow sphere depends on the specific scenario and the accuracy of the model. In some cases, it may have a minimal impact on the overall behavior of the sphere, while in others it may significantly alter the results. It is important to carefully consider the implications of removing these elements in any scientific or engineering application.

• Introductory Physics Homework Help
Replies
16
Views
714
• Introductory Physics Homework Help
Replies
1
Views
757
• Introductory Physics Homework Help
Replies
23
Views
985
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
359
• Introductory Physics Homework Help
Replies
3
Views
239
• Introductory Physics Homework Help
Replies
3
Views
410
• Introductory Physics Homework Help
Replies
11
Views
433
• Introductory Physics Homework Help
Replies
12
Views
2K