- #1

tsw99

- 35

- 0

## Homework Statement

Moment of inertia of spherical shell of radius R, mass M along its rotation axis is given by [tex]\frac{2}{3}MR^{2}[/tex]

I am trying to calculate this

## Homework Equations

## The Attempt at a Solution

This is my attempt but is unsuccessful,

since the spherical shell is an assembly of rings (of varying radius), and the MI of a ring is

[tex]I=MR^{2}[/tex]

Hence [tex]dI=y^{2}dm[/tex]

[tex]I=\int y^2(2\pi \sigma ydz[/tex]

Using [tex]y=Rsin\theta[/tex] and [tex]z=Rcos\theta[/tex]

I get:

[tex]I=2 \pi \sigma R^{4} \int sin^{4}\theta d\theta

=2 \pi \sigma R^{4} \frac{3\pi}{8}

=\frac{3\pi MR^{2}}{16}[/tex]

which is incorrect.

Which step I have gone wrong? Thanks

Last edited: