Moment of Inertia Problem

1. rwx1606

32
[SOLVED] Moment of Inertia Problem

1. The problem statement, all variables and given/known data
A compound disk of outside diameter 140.0cm is made up of a uniform solid disk of radius 50.0cm and area density of 3.00 g/cm^2 surrounded by a concentric ring of inner radius 50.0cm, outer radius 70.0cm, and area density 2.00 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
Moment of inertia of a solid cylinder: I=1/2MR^2
Moment of inertia of a thin-walled hollow cylinder: I=MR^2

3. The attempt at a solution
Well I don't really know how this thing looks. What I did was calculate the mass of the inner circle using the area density and then used the moment of inertia equation for a solid cylinder. Then I calculated the mass of the concentric ring using the given area density and calculated the area of this ring by subtracting the area solid disk from the concentric ring. Again, I used the moment of inertia of a thin-walled hollow cylinder for this part. The last part is finding the moment of inertia of the outer disc with the diameter of 140.0cm. There's no area density given for this outer disc so I don't know how to calculate its moment of inertia. Then again I could be approaching this whole problem wrong. Any help is appreciated!

Staff: Mentor

There are only two parts of the composite disk, the inner solid disk and the concentric ring. Note that the diameter of the concentric ring is 140 cm.

The composite disk looks like this:

..........OOOOOOOOO
.......OOOOOOOOOOOOOOO
.....OOOOOOOOOOOOOOOOOOO
...OOOOOOOOiiiiiiOOOOOOOOO
..OOOOOOiiiiiiiiiiiiOOOOOOO
..OOOOOiiiiiiiiiiiiiiiOOOOO
.OOOOOiiiiiiiiiiiiiiiiiOOOOO
.OOOOiiiiiiiiiiiiiiiiiiiOOOO
OOOOiiiiiiiiiiiiiiiiiiiiOOOOO
OOOOiiiiiiiiiiiiiiiiiiiiiOOOO
OOOOiiiiiiiiiiiiiiiiiiiiiOOOO
OOOOiiiiiiiiiiiiiiiiiiiiiOOOO
OOOOOiiiiiiiiiiiiiiiiiiiiOOOO
.OOOOiiiiiiiiiiiiiiiiiiiOOOO
.OOOOOiiiiiiiiiiiiiiiiiOOOOO
..OOOOOiiiiiiiiiiiiiiiOOOOO
..OOOOOOOiiiiiiiiiiiiOOOOOO
...OOOOOOOOOiiiiiiOOOOOOOO
.....OOOOOOOOOOOOOOOOOOO
.......OOOOOOOOOOOOOOO
..........OOOOOOOOO

The outer disk (50 cm inner radius, 70 cm outer radius) does not qualify as thin-walled. You need to use some other equation.

3. rwx1606

32
thanks a lot! I must have been reading the problem as a compound disk with an outside radius of 140.0cm instead of diameter. You picture was really helpful, and when I used the moment of inertia for a hollow cylinder I ended up with the right answer. Thanks a lot again!

Staff: Mentor

You're welcome. Thread marked as "solved".