# Moment of Inertia of a Curved Rod

Find the moment of inertia when the wire of constant density shaped like the semicircle
y=sqrt(r^2-x^2)
is revolved around the x-axis

I dont even know where to begin =[

berkeman
Mentor
Find the moment of inertia when the wire of constant density shaped like the semicircle
y=sqrt(r^2-x^2)
is revolved around the x-axis

I dont even know where to begin =[
Welcome to the PF. Start with the definition of the Moment of Inertia. What is it in the general case?

I'm also having a little trouble visualizing the shape... is there any way you can sketch it?

the general case for a thin rod is I=\int(mr^2)

but I don't know what it is for a curved rod. The rod in the problem is a semi circle about the origin in quadrants I and II with radius r

You have to do the integration from the definition of moment of inertia.

$$I\ =\ \int dm\ r^2\$$

Some tips: dm can be expressed in terms of linear density $$dm\ = \rho d\theta$$, with theta in play due to it being easier in this case to use polar co-ordinates.