Determining the center of mass experimentally

[JinM]

Hello!
How does one determine the center of mass of an irregular solid (with uniform density of course) experimentally? I know the plumb bob way, but I was wondering if there is another way?

Thanks,
Jin

 

[esalihm]

there is another way I know, but you will have to drill the solid for this :)
Lets consider a ruler with holes on it (I know this aint ireegular but just for simplicity)
You hang the ruler from one of the holes to a pin and see if it makes a 180 degrees turn.
If it doesnt, then you hang it from another hole that's below the one u used for the previous trial. U continue doing this until the object makes a 180 degree turn. When u get the turn, u ang it from a hole that's above the one u got the turn.

If you can manage to hang it from the hole that's right at the center of mass of the soid, it will stay still and not make turns

I know that isn't much practical with an irregular solid but just an idea!

 

[JinM]

Well, is there a more practical way? I'm just interested in how to find it experimentally.

 

[TVP45]

Well, is there a more practical way? I'm just interested in how to find it experimentally.

I don't know the plumb bob way. How does that work?

There is a way, but it's not always practical. You can float the object (plus a dangling weight) such that half the object is above and half below (this takes some calculating). Do this for several planes and they intersect at the CM. Now, where you get the liquid (mercury?) is another story.

 

[belliott4488]

I don't know the plumb bob way. How does that work?

This is fairly easy for a 2-d object. You just push a pin through the object (say, a cut-out map of Texas) and hang it on a cork board leaving it free to rotate. The CM will be below the suspension point, so hang a plumb bob from the pin and draw a line along the string that's suspending it. Repeat for another point of suspension, and then for a third, as a check. All the lines you've drawn should intersect at one point, which is the CM.

In 3-d you can do the same thing, it just gets tricker because the object isn't flat (in general), so you can't necessarily hang it against a board. I'd say just hang it from from various points on it surface, and then cleverly find a way to project a line from a plumb bob hanging right next to the object onto the surface of the object, such that the projected line goes through the point of suspension. (Laser? Spray paint?) You could to this for a single suspension point, while moving the plumb bob to different sides, and then repeat for different suspension points. You should end up with a bunch of lines drawn on the surface of the object. Connect their intersection points with imaginary lines through the interior of the object, and that should be your CM. Make sense?