I created a UVsphere with segs=rings=5, no matter I chose the 3- or 4-vertex face ,Curs -> Sel did not shift the cursor to the face, and even not on the normal of the face %|
Then how to place the cursor to the center of mass?
It should put the 3d cursor wherever the currently selected object’s centre is. If the selected object’s centre point isn’t in the centre (eg, if you’ve extruded it/scaled it in one direction) try ‘centre new’ on the Edit Buttons and then try Curs->Sel.
Hope that helps 
Hmm, I just tried this on a 5 segments, 5 rings UVSphere and after selecting a 4 vertice face and pressing Shift_s > Cursor to Selection, it does seem to place the 3DCursor outside of the face.
Is this a bug?
Anyway, you could use this work-around technique:
[>] Add a mesh UV Sphere: 5 segments, 5 rings ,
[>] Pick a face (one with 4 vertices) that you want your circle to lie upon), select the ‘top’ 2 vertices; then Shift_s > Cursor to Selection, Add an Empty.
[>] Re-select the UVsphere, select the ‘lower’ 2 vertices of the face; then Shift_s > Cursor to Selection, Add an Empty.
[>] Select the 2 Empties, then Shift_s > Cursor to selection.
[>] Delete the 2 Empties and reselect the UVSphere.
<EDIT>
Arrgghh
I think I just figured out something.
Still not exactly sure how or why it works that way, but :
On the 3D Window header, there is a group of 4 buttons that control the scale/rotate with respect to mode of operation. By default the first one is selected: (Tool tip = ‘Enables Rotation or Scaling around bound box center COMMA key’)
For whatever reason, you need to select the second button with the Tool tip: (‘Enables Rotation or Scaling around median point’)
BEFORE you activate the Shift_s > Cursor to Selection function.
I believe when you do this it takes a weighted average of the vertice’s location to determine the center point.
For example -> starting with a default blend file, with the default plane,
[>] enter Edit mode,
[>] select the ‘top’ 2 vertices and scale them down to zero,
[>] perform a ‘remove doubles’ operation => You should now have a triangle,
[>] compare what happens when you do a Shift_s > Cursor to Selection operation, when you have the first or second ‘Scale/Rotate’ wrt button pressed.
With the first button, the cursor remains at the origin;
With the second button pressed, the cursor is shifted to the lower part of the triangle.
ie. in the first case, Blender just looks at the ‘bound box’ of the selection " the point furthest to the top and the point furthest to the bottom (same for to the left and the right) and averages them; thus the cursor remains at the origin.
In the second case, Blender takes a weighted average of the 3 vertices, and since there are 2 vertices at the bottom vs. one at the top, the cursor is shifted down a bit.
</EDIT>
WooHoo, I think I learned something today 
Yeah, I think I learned more: center new + scale/rotate center mode
its like “snap to” in PS