This was a 2 part problem...(adsbygoogle = window.adsbygoogle || []).push({});

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}pdV. So I integrated 1/2y^{2}ppiy^{2}dz and substituting density forp=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(p4/3piR_{m}^{3})R^{2}-2/5(p4/3piR_{m}^{312})R^{23}

wherep=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...

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# Homework Help: Moment of Inertia for Earth by superposition

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