# How to find centre of gravity for a hemisphere shell?

• mick_1
In summary, the conversation discusses how to find the centre of gravity for a hemisphere shell. The suggested method is to integrate the mass density over the surface for each axial direction. Another suggestion is to use the symmetry of rotation around the z-axis to simplify the problem to finding the centre of mass for a semicircle. However, there is a discrepancy between the results obtained from integration and the symmetry argument. The conversation ends with a request for clarification on this issue.
mick_1
How to find centre of gravity for a hemisphere shell??

Can someone show me how to calculate centre of gravity for a hemisphere shell??

These sound suspiciously like homework problems.

It's not homework, I'm preparing for an examination. And I have serious problem solving this assignment. Pleas help me!

Integrate mass density over the surface for each axial direction. As far as I can remember for rectangular coordinates its

$$y_{cm} = \int{\rho(x) f(x)dx}$$

$$x_{cm} = \int{\rho(x) xf(x)dx}$$

but my memory is probably mistaking me. There should be an example of this in your book though.

Here's the hint:use the rotation around Oz symmetry to transform your problem into a very simple one:finding the C of M for a semicircle of radius R.You basically need the "z" coordinate of the C of M for the hemisphere,or the "y" coordinate for the C of M for the semicircle.

Daniel.

The result obtained from integration and your symmetry argument are NOT the same.
For a semicircular wire, the COM is $$(0, \frac{2R}{\pi})$$ while from integration, it is $$(0,0,R/2)$$. Can anybody explain this?

I know this is an old post, but I have been struggling with the same problem for a while now , can anyone explain this?

## 1. How do I determine the center of gravity for a hemisphere shell?

The center of gravity for a hemisphere shell can be determined by finding the geometric centroid of the shell. This can be done by dividing the shell into smaller, more manageable shapes (such as triangles) and finding the centroid of each shape. The overall centroid of the hemisphere shell will be the average of all the individual centroids.

## 2. Can the center of gravity for a hemisphere shell be located at a point outside of the shell?

No, the center of gravity for a hemisphere shell will always be located within the shell itself. This is because the center of gravity represents the point at which the weight of the shell is evenly distributed in all directions.

## 3. Is there a specific formula for calculating the center of gravity for a hemisphere shell?

Yes, there is a formula for finding the center of gravity for a hemisphere shell. It involves using the dimensions and weight of the shell to calculate the centroid of each smaller shape and then averaging them to find the overall centroid. It is a complex calculation and may be easier to use computer software or consult a professional.

## 4. Is the center of gravity in the same location for all hemisphere shells?

No, the center of gravity for a hemisphere shell will vary depending on the dimensions and weight of the shell. A larger, heavier shell will have a different center of gravity compared to a smaller, lighter shell.

## 5. Why is it important to know the center of gravity for a hemisphere shell?

Knowing the center of gravity for a hemisphere shell is important for understanding its stability and balance. This information can be useful in designing and constructing structures or objects that use hemisphere shells, such as domes or tanks. It can also help prevent accidents or damage caused by an unbalanced or incorrectly placed shell.

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