Moment of Inertia of a Curved Rod

[sunniexdayzz]

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

I don't even know where to begin =[

 

[berkeman]

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

I don't 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?

 

[sunniexdayzz]

the general case for a thin rod is I=\int(mr^2)
with m=mass and r=radius

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

 

[Beam me down]

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.