- #1

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PART A: calculate moment of inertia of a uniform sphere of mass M and radius R by using the information provided:

the moment of inertia of a thin spherical shell at radius R with mass m spinning about its axis is 2/3mR

^{2}.

I did this by integrating over thin shells with density,

*p*, from radius -R to R.

Knowing that dI=1/2y

^{2}dm=1/2y

^{2}

*p*dV. So I integrated 1/2y

^{2}

*p*piy

^{2}dz and substituting density for

*p*=M/(4/3)piR

^{3}

the answer I got was 2/5piR

^{2}

PART B: (this was where I started having difficulty understanding..) you can calculate the moment of inertia of a layered Earth model by superposing the results for a uniform sphere. The moment of inertia of a 2 layer Earth model with a core of mass M

_{1}and an outer shell mass M

_{2}separated at radius R

_{12}and a total radius of R is given by:

EQUATION #1--->

I=2/5M

_{1}R

^{212}+2/5(

*p*4/3piR

_{m}^{3})R

^{2}-2/5(

*p*4/3piR

_{m}^{312})R

^{23}

where

*p*=density of mantle.

_{m}(below is copy-pasted equation from hw sheet...not sure which one is easier to read)

I =

2

5

M1R2

12 +

2

5

(m

4

3

R3)R2 −

2

5

(m

4

3

R3

12)R2

12

It tells me to derive equation #1(above) by superposition

I have no idea where to get started on this part...