Moment of Inertia of a Curved Rod

  • #1
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 dont even know where to begin =[
 

Answers and Replies

  • #2
berkeman
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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 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?
 
  • #3
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
 
  • #4
You have to do the integration from the definition of moment of inertia.

[tex]
I\ =\ \int dm\ r^2\
[/tex]

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

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