Posted by **Chris** on Sunday, June 10, 2012 at 5:44pm.

The figure shows a uniform disk with a circular hole cut out of it. The disk has a radius of 4.00 m. The hole's center is at 2.00 m, and its radius is 1.00 m. What is the x-coordinate of the center of gravity of the system?

The center of the disk is (0,0)

The center of the hole is at (2,0)

- Physics! -
**Elena**, Sunday, June 10, 2012 at 6:18pm
x1=0, y1=0, x2=2m, y2=0.

R=4 m, r=1 m.

y(c.m.) =0

x(c.m.) = (A1•x1 –A2•x2)/(A1-A2)=

=(A1•0-A2•x2)/(A1-A2)

= - πr²•2/π(R²-r²) =

= - 1•2/(16-1) =2/15 = - 0.133 m

Center of mass x=- 0.133 m, y = 0

- Physics! -
**Count Iblis**, Sunday, June 10, 2012 at 6:20pm
Hint: If you take the equation for the cente of the mass, and you multiply that by the total mass, you get:

Integral of rho(r) r d^3r

This satisfies the superposition principle, the result for a density function rho1 + rho2 is the same as that for rho1 and rho2 seperately and then added together.

This means that you can add up the what you get for a disk without a hole to what you get for a hypothetical disk of negative mass. You then divide the result by the total mass.

## Answer This Question

## Related Questions

- physics - A curcial part of a piece of machinery starts as a flat uniform ...
- Physic - A machine part is made from a uniform solid disk of radius R = 0.161 m ...
- Physics - A machine part is made from a uniform solid disk of radius R and mass ...
- Physics - A thin rectangular plate of uniform area density σ1 = 1.01 kg/m2 ...
- physics - A thin rectangular plate of uniform area density σ1 = 1.00 kg/m2 ...
- physics - A spherical shell of uniform charge density σ has a circular hole...
- physics - A spherical shell of uniform charge density σ has a circular hole...
- Physics - A solid cylindrical disk has a radius of 0.18 m. It is mounted to an ...
- physics - A solid cylindrical disk has a radius of 0.17 m. It is mounted to an ...
- Physics - The figure shows three rotating, uniform disks that are coupled by ...

More Related Questions