How to find centre of gravity for a hemisphere shell?

[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??

 

[SpaceTiger]

These sound suspiciously like homework problems.

 

[mick_1]

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

 

[whozum]

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.

 

[dextercioby]

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.

 

[GPhab]

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?

 

[Idoubt]

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