# Inertia of weighted rings

1. Dec 8, 2008

### cantgetno

1. The problem statement, all variables and given/known data
A compound disk of outside diameter 138 cm is made up of a uniform solid disk of radius 39.0 cm and area density 5.40 g/cm^2 surrounded by a concentric ring of inner radius 39.0 cm, outer radius 69.0 cm, and area density 2.60 g/cm^2.

Find the moment of inertia of this object about an axis perpendicular to the plane of the object and passing through its center.

2. Relevant equations
I=m r^2
area = pi r^2

3. The attempt at a solution

Mass

pi x 39^2 = 4778 cm2
4778x5.40 = 25801.2g =25.801kg

pi x 69^2 (-4778) = 10179cm2
10179x2.60=26465.4g =26.465kg

i now dont understand how to work out the inertia

2. Dec 8, 2008

### Staff: Mentor

Look up the formula for the moment of inertia of a disk and a ring.

3. Dec 8, 2008

4. Dec 8, 2008

### cantgetno

I= 0.5 m r^2
I = 0.5 x 25.8 x 39^2 = 1920.9

And for the other:
I= 0.5 m(r1^2 + r2^2)
I=0.5 x 26.465 x (39^2 +69^2) = 83126.6

do i add these together? giving
102747.465 ?

5. Dec 8, 2008

### LowlyPion

Yes the moments about the same point add for a compound moment.