Find the Moment Inertia of a Cross Section: y = 30 & 35

• ricky_fusion
In summary, Ricky says that he doesn't know how to calculate the distance from the center of mass to the model. He wants to know if the model is symmetric and if it is possible to calculate the I on the basis of the double integral over the distribution of mass about the centroid point.

ricky_fusion

Hi..
I've got a problem about moment inertia. I don't understand about looking the distance of centroid (y). I am still confucing about the formula of "y" in Moment Inertia. Can you shows me about the formula of y or if any thread for this before, I am glad to see it too.Thanx's for your help..
I still don't know how to find put y =30 and 35

Homework Statement

Known : You can see the dimension and the picture in my attachment
Asking: How is to calculate y ?? Is the formula same to all geometry??

I = y dA

The Attempt at a Solution

Cross section
Total Area: - A =>40*60=2400
- y => 30 Why is it 30?
- Ay =>72000
Inside Area:-A=> -20*30=-600
-y =>35 Why is it 35?
- Ay => -21000

Attachments

• Moment.jpg
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Ricky, we can't see the picture until one of the tutors comes on line to release it.
If you are in a hurry, you could post the picture to photobucket.com and give us a link.

Apparently you want the moment about the center of mass.

In which case you need to determine the center of mass (centroid point) and then calculate the I on the basis of the double integral over the distribution of mass about that point.

You can also exploit the symmetry that the objects present, if you consider that they can be broken up into 4 rectangles, and use the parallel axis theorem to determine the sum of the system. (Since you have some asymmetry you may need to do it in steps.)

Hmm..
I knows about it, but I just don't knows how to calculate the distance from center of mass to the model. I meant from this formula "I = y dA." How is to calculate "y"?? Becauses I don't have some information about it. How to find out the distance in I,T,U or not simetric model?? I knows that to find out "I", I should divide the model into 2-3 section, but after that how to calculate the "y" before I apply it into the moment Inertia formula (I = y dA)??

What is moment of inertia and why is it important?

Moment of inertia is a measure of an object's resistance to changes in rotational motion. It is important because it helps determine an object's stability, strength, and ability to resist bending or breaking.

How do you calculate moment of inertia?

The moment of inertia of a cross section can be calculated by integrating the area of the cross section multiplied by the square of the distance from the axis of rotation.

What is the formula for moment of inertia of a cross section with a y = 30 & 35?

The formula for moment of inertia of a cross section with a y = 30 & 35 is I = ∫(y^2)dA, where y is the distance from the axis of rotation and dA is the differential area of the cross section.

What are the units of moment of inertia?

The units of moment of inertia depend on the units of the area and distance used in the calculation. Generally, the units are represented as length^4, such as m^4 or in^4.

How does the shape of a cross section affect its moment of inertia?

The shape of a cross section directly affects its moment of inertia. A cross section with a larger area and a greater distance from the axis of rotation will have a higher moment of inertia, making it more resistant to changes in rotational motion. Similarly, a cross section with a smaller area and a shorter distance from the axis of rotation will have a lower moment of inertia and be less resistant to changes in rotational motion.