78. Finding centers to incongruent shapes

[mklotz]

Thinking out loud here...

The "center" you're looking for is the center of mass. Suspend the object by hanging it on a plumb bob cord above the bob. Now, the object must hang with its CM below its suspension point. That means the cord must pass over the CM location. Draw a line along the cord.

Now repeat this process while supporting the object from a different point. Where the two lines cross is the CM of the object.

Obviously, this method won't work for unwieldy or super heavy objects and something like that posted in the OP will be needed. I just wanted to throw this idea out to see if anyone can use it to make some clever tool.

On further thought...

It would probably be easier to just pin the object to the wall with a single pivot and let it hang free. Then hold a plumb line to the pivot and use it to mark a point on the object opposite the pivot point. Later, a line drawn through this mark and the pivot point will pass though the CM.

As above, repeat with a different pivot point. The CM is located where the two lines cross.