Relationship between mass moment of inertia and second moment of area?

In summary, the conversation revolves around creating a model in SimMechanics and the use of mass and inertia tensor. The textbook and Simscape use different units and there is a question about the relationship between area moment of inertia and mass moment of inertia. The conversation concludes with the fact that they are independent but still related to each other through the area density.
  • #1
Fat Ryan
50
0
I am trying to create a model in SimMechanics of a simple damped frame. I am very new to this software and structural dynamics as well. I have a copy of "Dynamics of Structures" 3ed by Chopra. In the textbook, the author uses the standard geometric and material properties that I am familiar with to obtain stiffnesses (modulus of elasticity, E & second moment of area, I). Simscape, however, asks for mass and inertia tensor. The latter of which has units of mass*length^2. Is there some sort of relationship between the area moment of inertia and mass moment of inertia? The reason it of importance is because I need to create this model and verify it somehow. If I replicate an example in the textbook, then obviously I'll know if I'm doing things correctly. Unfortunately, the textbook only provides area moment of inertia in it's examples.
 
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  • #2
Sorry, the two are totally independent of each other.
 
  • #3
viscousflow said:
Sorry, the two are totally independent of each other.

hmm, does anyone know why there's a difference between the book and simscape then?
 
  • #4
viscousflow said:
Sorry, the two are totally independent of each other.

This isn't really true...

They are different, but still dependent/related to each other...
I've never found this in a book,
but one can show the relation between them by using balance of linear momentum...

The relation is the following:

Imass = [tex]\rho[/tex]area * Iarea

where

Imass : Mass Moment of Inertia
Iarea : Area Moment of Inertia
[tex]\rho[/tex]area : area density (kg/m²)
 
  • #5
Assuming constant density...
 
  • #6
enigma said:
Assuming constant density...
Yes, I forgot to mention that. Thanks!
 

1. What is the difference between mass moment of inertia and second moment of area?

The mass moment of inertia, also known as the rotational inertia, is a measure of an object's resistance to rotational motion. It takes into account the distribution of mass and the distance from the axis of rotation. On the other hand, the second moment of area, also known as the moment of inertia, is a measure of an object's resistance to bending under an applied load. It takes into account the shape and size of the cross-section of an object.

2. How are mass moment of inertia and second moment of area related?

The mass moment of inertia and second moment of area are related through the equation I = mk^2, where I is the mass moment of inertia, m is the mass of the object, and k is the radius of gyration. The radius of gyration is a measure of how far the mass is distributed from the axis of rotation, and is related to the second moment of area.

3. Why is it important to consider the relationship between mass moment of inertia and second moment of area?

The relationship between mass moment of inertia and second moment of area is important in understanding an object's response to rotational and bending forces. It allows engineers to design structures and machines that can withstand these forces without failing or experiencing excessive deformation. It also plays a crucial role in predicting the stability and performance of rotating objects.

4. How does the shape of an object affect its mass moment of inertia and second moment of area?

The shape of an object has a significant impact on both its mass moment of inertia and second moment of area. Objects with a larger cross-sectional area and mass that are distributed further from the axis of rotation will have a higher mass moment of inertia and second moment of area. This means they will have a greater resistance to rotational and bending forces.

5. How can the relationship between mass moment of inertia and second moment of area be used in real-life applications?

The relationship between mass moment of inertia and second moment of area is used in various real-life applications, such as designing high-performance vehicles, calculating the stability of buildings and bridges, and predicting the behavior of rotating machinery. It is also used in sports equipment design, such as designing golf clubs with the right amount of rotational inertia for optimal performance.

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