Center of mass of non-uniform plate

[Arun Veera]

Hello Bruce .. I have problem regarding finding the center of mass of a rectangular plate practically. Also it is a geometric property i.e it mid point is the COM . but the plate is not homogeneous and high dense regions occur at the plate at some portions of the plate ... SO my COM is not at the midpoint , suggest a way to find the COM ... Thank you!

 

[TumblingDice]

I have problem regarding finding the center of mass of a rectangular plate practically. Also it is a geometric property i.e it mid point is the COM . but the plate is not homogeneous and high dense regions occur at the plate at some portions of the plate ... SO my COM is not at the midpoint , suggest a way to find the COM ... Thank you!

Do you need COM in all 3 dimensions of the plate, or just across the 2D plane? If just 2D, can you spin it on a slick surface long enough to mark the center of rotation?

 

[sophiecentaur]

Alternatively, you can balance it over a straight edge, at two different angles. Where the lines intersect will be the CM. Or you can hang the plate from a point near the edge and draw a line on it using a plumb line (chalked, like when you are decorating). Do this twice and the two lines will intersect on the CM.
In 3D, it's harder but could involve suspending the plate, again using a plumb line. If you suspend the plate from front and back edges, that will tell you whether the CM is actually in the plane in the centre of the two faces. It depends on how think the plate is as to whether that's relevant.

If your plate has cut-outs, it is just possible that the CM may lie actually in one of the cutouts. That would be interesting.