Center of Mass Homework: Equations & Solution

[snowcover]

Homework Statement

Homework Equations

Please see attachment to #3.

The Attempt at a Solution

Apparently, the answer is Y= 4R/(3*pi). Why?

 

[kuruman]

Apparently, the answer is Y= 4R/(3*pi). Why?

You are asking the wrong question. The right question to ask is, "Where did I go wrong?" You went wrong in that you did not calculate the x and y components of the center of mass vector. You need to calculate the x and y components of that vector separately.

 

[snowcover]

Thanks. I separated vector r into x and y components, integrated, and I got it.

I guess my first attempt did not work because even though I tried to do a conversion at the end...I needed to integrate r as a vector first because its components change as the angles change.

 

[kuruman]

I guess my first attempt did not work because even though I tried to do a conversion at the end...I needed to integrate r as a vector first because its components change as the angles change.

You got it. It's a common mistake to do what you did. Now you know better.