Question

The center of mass of quarter circle y=sqrt( r^2 -x^2) is given by the point??

Answer 1

\[y= \sqrt{r^2 - x^2} , x \in[0,r] \]

Answer 2

so what troubles you having?

Answer 3

do you know the formula to find the center of mass?

Answer 4

like are you having trouble at a certain spot?

Answer 5

\[\text{ Let's call the point } (x',y') \\ x'=\frac{1}{A} \int\limits_a^b x (f(x)-g(x)) dx \\ \text{ and } \\ y'=\frac{1}{A} \int\limits_a^b \frac{1}{2}([f(x)])^2-[g(x)]^2) dx\]

Answer 6

A represents the area of the quarter circle

Answer 7

f(x)=sqrt(r^2-x^2)
and g(x)=0

Answer 8

let me know if you have any troubles

Answer 9

thank you. would A just be pi(r)^2 / 4 ?

Answer 10

yes