The x,y,z coordinates of CM of a solid cylinder

  • #1
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I have found via integration that the y coordinate is $$y =h/2 = 120 mm$$. The x coordinate is $$x = \frac{-4r}{3\pi} = -51.9mm$$ and the z coordinate is $$z = r - \frac{4r}{3\pi} = 69.1 mm$$. I have no answers in my textbook so cant confirm whether i am correct or not.
 
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  • #2
SteamKing
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Google is you friend here.
 
  • #3
Baluncore
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If the cylinder is complete then the centre of mass is the midpoint.

If it is a quadrant of a solid cylinder as shown in your picture then it will be at C.y = h/2 as you show. The CM will lie on the plane of symmetry at 45 degrees, so the C.x and C.y offsets from the cylinder axis should have identical values. I suspect your values are correct.
Would it not be easier if you placed your origin and z axis on the cylinder axis ?

The centroid of a cylindrical segment, hoof or wedge is available on Wolfram Alpha. http://mathworld.wolfram.com/CylindricalSegment.html
Unfortunately the quarter tank problem has only one plane cut. You need two.
But one of the values will be the same as for a half cylinder which has a single plane cut.
 
  • #4
Baluncore
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Your values appear to be correct. Attached is a one page extract from an 8MByte .pdf

There is an even easier solution.
The centroid of a semicircle is R * 4 / 3π
 

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