Uniform Lamina

1. Nov 3, 2005

brandon26

Where is the centre of mass of a semicircular lamina which is uniform? I know it is somewhere along the line of symestry, but where excactly?

2. Nov 3, 2005

Fermat

It only takes a few moments to work it out.
com = 4r/3pi

3. Nov 3, 2005

brandon26

Can you be of more help please?

4. Nov 3, 2005

Fermat

Of course. Drag your mouse over the answer in my last post.

5. Nov 4, 2005

HallsofIvy

Surely, if you have a question like that, you know the basic formulas.

The y-coordinate of the centroid of a region (center of mass assuming uniform density) is $$\frac{\int y dA}{\int dA}$$.
$$\int dA$$ is, of course, the area of the region.

Once, when I was teaching this, a student became fascinated by the word "lamina" (had never seen it before, apparently). As the last question on the final exam, I asked "What is 'lamina' spelled backwards?"

Another student became furious with me because "That question doesn't make any sense!"

6. Nov 8, 2005

brandon26

Oh sorry. Haha. I didnt realise there was invisible ink on the paper.