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Center of mass of a cone 
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#1
Oct1805, 07:37 PM

P: 22

I need to find the center of mass of a cone with point facing downwards, of height H and radius R.
Since the density is constant throughout and because of axial symmetry the center must be somewhere on the zaxis. I know from convention that this is H/4 but i need to derive this. Rcm = (intregral from 0 to H) of the change in radius this is where im stumped i did really bad in calculus could anyone help me? 


#3
Oct1805, 08:00 PM

P: 211

Let Dv Be An Element In The Form Of A Disk That Cuts Through The Cone.
The Radius Of The Disk Is (r / H) X. The Volume Equals The Area Of The Disk Times The Thickness. Dv = Pi[(r / H ) X] ^2 Now Intergate From 0 To H X' = Int (x Dv) / Int Dv = 3/4 H 


#4
Oct1805, 08:00 PM

P: 22

Center of mass of a cone
okay so the biggest such disk would have volume pi*R^2*h
what is the volume of the disk under that? 


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