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- Homework Statement
- Please see below

- Relevant Equations
- Please see below

For this problem,

How do we calculate the moment of inertia of (2) and (3)?

For (3) I have tried,

##I_z = \int r^2 \, dm ##

## ds = r ## ##d\theta ##

##\lambda = \frac {dm}{ds}##

##\lambda ## ##ds = dm ##

## \lambda r ## ##d\theta = dm ##

##I_z = \lambda \int r^3 d\theta ##

##I_z = \lambda \int_0^{2\pi} r^3 d\theta ##

EDIT:

I know how to find the moment of inertia of (3) (shown in post ##2), however, how do I find the moment of inertia of the square about z-axis?

Many thanks!

How do we calculate the moment of inertia of (2) and (3)?

For (3) I have tried,

##I_z = \int r^2 \, dm ##

## ds = r ## ##d\theta ##

##\lambda = \frac {dm}{ds}##

##\lambda ## ##ds = dm ##

## \lambda r ## ##d\theta = dm ##

##I_z = \lambda \int r^3 d\theta ##

##I_z = \lambda \int_0^{2\pi} r^3 d\theta ##

EDIT:

I know how to find the moment of inertia of (3) (shown in post ##2), however, how do I find the moment of inertia of the square about z-axis?

Many thanks!

Last edited: