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

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1. Apr 30, 2015

HMPARTICLE

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.

Last edited: Apr 30, 2015
2. Apr 30, 2015

SteamKing

Staff Emeritus

3. May 2, 2015

Baluncore

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. May 2, 2015

Baluncore

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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• SemiCylinder.pdf
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Last edited: May 2, 2015