Finding the center of mass by integration.

[tfmfyn]

Homework Statement

Show that the center of mass of a uniform semicircular disk of radius R is at a point 4R/(3(pi)) from the center of the circle.

Homework Equations

Total mass Center of mass = M rcm = m1r1 + m2r2 + ...

The Attempt at a Solution

I do not know how to apply integration to this problem to find the center of mass. Help, please?

 

[Dick]

Don't you have any integral expressions for center of mass?

 

[tiny-tim]

Hi tfmfyn!

Hint: divide the semicirce into slices of thickness dz parallel to the base, find the mass of each slice, and integrate … something … over dz.