# 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.