Moment of Inertia for a Sphere with Lead Coating

[MAPgirl23]

A sphere consists of a solid wooden ball of uniform density 800 kg/m^3 and radius 0.20 m and is covered with a thin coating of lead foil with area density 20 kg/m^2.

How do I calculate the moment of inertia of this sphere about an axis passing through its center?

** The equation I'm using for the solid sphere is I = 2/5 * M * R^2
Here again I know the mass of the inner sphere is the density times the volume of the sphere. They gave me the area density for the layer of lead, so you can find the mass of the lead using the area density times the surface area of the sphere. By definition of moment of inertia, the total moment of inertia of the sphere is the sum of the moment of inertia of the solid wood part, plus the moment of inertia of the lead shell. Is this method wrong? Do you not get the moment of density this way without being given mass but instead given density?
Please help.

 

[arildno]

A sphere consists of a solid wooden ball of uniform density 800 kg/m^3 and radius 0.20 m and is covered with a thin coating of lead foil with area density 20 kg/m^2.

How do I calculate the moment of inertia of this sphere about an axis passing through its center?

** The equation I'm using for the solid sphere is I = 2/5 * M * R^2
Here again I know the mass of the inner sphere is the density times the volume of the sphere. They gave me the area density for the layer of lead, so you can find the mass of the lead using the area density times the surface area of the sphere. By definition of moment of inertia, the total moment of inertia of the sphere is the sum of the moment of inertia of the solid wood part, plus the moment of inertia of the lead shell. Is this method wrong?

No, this is a correct method.

Do you not get the moment of density this way without being given mass but instead given density?

I'm sorry, I don't understand your question.

 

[Dr.Brain]

The answer= MI of wooden solid sphere+ MI of lead shell

 

[MAPgirl23]

volume of sphere: 4/3 * pi * r^3
surface area sphere: 4 * pi *r^2

mass of lead: 20 * (4 * pi * 0.2^2) = 10 kg
mass of sphere: 800 * (4 * pi * 0.2^2) = 26.8 kg

I solid sphere: 2/5 * 26.8 * 0.2^2 = 0.429
I lead shell: what do I use?

 

[Nylex]

I lead shell: what do I use?

$$I = \frac{2}{3}MR^2$$

 

[dextercioby]

Incidentally,the sphere has zero volume and its moment of inertia wrt an axis passing through its center is given in post #5.

BTW,what do you mean by solid sphere,is it a special sphere,i dunno,similar to a plasma or liquid one...?

Daniel.

 

[Nylex]

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