Finding Centre of Mass for a Uniform Semicircular Lamina

[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?

 

[Fermat]

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

 

[brandon26]

Can you be of more help please?

 

[Fermat]

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

 

[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!"

 

[brandon26]

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

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