Understanding how to set up integrals for inertia

AI Thread Summary
To set up integrals for calculating the inertia tensor, one must first define the inertia element and then integrate over the object's volume. For a disk, the limits for the xy-plane are determined by the circular area, while the z-axis limits depend on the thickness of the disk. The choice of coordinate system is crucial as it affects the limits of integration. Understanding the geometry of the object is essential for correctly setting up these integrals. Properly defining these parameters will facilitate accurate calculations of the inertia tensor.
jtandron
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Hello, and thank you in advanced for this. I am having trouble with setting up most if not all of my integrals when I am trying to find the elements of an inertia tensor. What would I do if i need to find say the tensor for a disk, but i don't know what to take for my three limits to be. i get that for the xy-plane it should be the circular area, but then for the z-axis? my head can't wrap itself around it. Again, please if you could shed me some help i thank you very much for it.
 
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Welcome to PF;
See: http://www.maths.tcd.ie/~kovacs/Teaching/Mechanics/tensor_inertia.pdf

Basically you construct the inertia element, then you add up all the lements - this will normally involve integrating over the volume of the object in question. The exact limits depend on the coordinate system and the extent of the object ... just like any volume integral.
 
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