How To Find The Centroid Of A Semicircle

Centers of semicircles and hemispheres Where is the center of the semicircle? If you cut a semicircle from a piece of cardboard of uniform density, would you be able to carefully balance it on top of a pin? If you don’t know the answer, think about it for a few seconds. Does your intuition give you a clue? Reading passage: how to find the center of a semicircle

Solution

Let’s use some math to figure out the answer: We can model a semicircle as a stack of extremely small thin bands. If we sum the times of all these bands, normalized over the area of ​​the entire semicircle, we can find the center. The center is the place where we can model the shape as if all the weight was acting through this point. We just need to determine how far this point is. This is about 42.44% of the radius Read more: how to fillet catfish with an electric knife I don’t know about you, but this answer surprised me a bit. I wouldn’t predict it would be an absurd percentage.

Switch to 3D

If a semicircle is extruded into a dome (uniform density), the center of the circle will be 42.44% of the base. But where is the center of a hemi sphere? Is it the same? Watch…

Hemisphere

Do you think this shape will have a different center? As before, we can model it as an infinitely small stack of thin circular pancakes stacked on top of each other. We can sum the times of all these disks and divide by the volume of half the sphere. Read more: How long does it take for shroom to launch This is 37.50% of the radius, which is an interesting result. It’s a bit cleaner than the formula for the semicircle and doesn’t involve the number π. Centroid is a little closer to the bottom of the dome. Is this the result you expected? It makes sense to assume that a hemisphere tapers along two axes as it moves from foot to vertex, so we should expect the center to be closer to the bottom. You can find a complete list of all articles here. Click here to receive email notifications of new articles. Read more: how to track changes in the page

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