Video about how to find centroids?

[thharrimw]

dose anyone know a website that has a video about how to find centroids?

 

[adriank]

I assume you want to find the centroid of a triangle. What, exactly, do you mean by finding a centroid? What are you given?

If you're given the coordinates of the vertices of a triangle, then just take their average to obtain the coordinates of the centroid.

 

[thharrimw]

F(x)= any equation over an interval for an example
F(x)=x^2 for [4,8]

 

[fredoniahead]

Try YouTube. They have lots of math videos.

But here is an example I will make up.

Find the centroid of the semicircular region with radius a centered at the origin.

By symmetry, the x-coordinate of the centroid is 0 since the y-axis is a line of balance.

[tex]\overline{y}=\frac{1}{\text{area of region}}\int\int_{R}ydA[/tex]

The area of a semicircle is [tex]\frac{{\pi}a^{2}}{2}[/tex]

So, we get, using polar coordinates and the fact that [tex]y=rsin{\theta}[/tex]

[tex]\frac{2}{a^{2}{\pi}}\int_{0}^{\pi}\int_{0}^{a}r^{2}sin{\theta}drd{\theta}=\frac{4a}{3\pi}[/tex]

So, the centroid is [tex]\left(0,\frac{4a}{3\pi}\right)[/tex]

Let's say the radius is a=1, then the coordinates of the centroid would be

(0,.4244)

 

[fredoniahead]

I found this on YouTube: