# Homework Help: Centre of mass

1. Oct 6, 2008

### ritwik06

1. The problem statement, all variables and given/known data
Center of Mass of a hemisphere

http://www.goiit.com/templates/default/images/chapters/center_mass/image064.gif [Broken]
http://www.goiit.com/templates/default/images/chapters/center_mass/image068.gif [Broken]
Why is volume of elemental disc = $$Rd\theta (cos \theta) (\pi R^{2}cos^{2} \theta)$$ and not

$$Rd\theta (\pi R^{2}cos^{2}\theta)?$$

Last edited by a moderator: May 3, 2017
2. Oct 7, 2008

### gabbagabbahey

Because the arc length is measured from the $\theta=0$ plane (yz plane) to the plane rotated through an angle $d\theta$, So the radius of the arc is the projection of R onto the $\theta=0$ plane which is $Rcos(\theta)$ and so the arc length is $Rcos(\theta)d\theta$.

3. Oct 7, 2008

### ritwik06

I dont get it. Could you please take some of ur precious time out, just to draw a very rough sketch in paint? Please!!