Moment of Inertia: Does Mass Matter?

In summary, the moment of inertia (or mass moment of inertia) of an object depends on its total mass, regardless of the chosen axis. The formula mentioned in the conversation is for area moment of inertia, which is used for predicting resistance to bending. Mass moment of inertia is used in rotational dynamics and takes into account the mass of the rotating object.
  • #1
mnandlall
12
0
Hello,

I was wondering if the moment of inertia of a 2-D triangle about its center of mass depends on the actual mass of the triangle. Formulas that I have found say that I = (bh^3)/36. Does this mean that the moment of inertia of triangles with the same dimensions will be the same about their center of mass regardless of their actual mass? I know that if you were taking the moment of Inertia about an arbitrary axis then the mass would come into play, according to the parallel axis theorem, but I'm not so sure about it when the inertia is about the center of mass.

Any help clearing this matter up for me would be appreciated.
 
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  • #2
different "moments of inertia"

The moment of inertia (a.k.a., mass moment of inertia) of any object most certainly depends on its total mass, regardless of chosen axis. That formula looks like an area moment of inertia (a.k.a, second moment of inertia), which is something quite different from "ordinary" moment of inertia and is used to predict resistance to bending. See: http://en.wikipedia.org/wiki/Second_moment_of_area" [Broken]
 
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  • #3
Alright, this makes a lot of sense. Thanks for clearing that up.
 
  • #4
Please don't get confused with the area M.I & mass M.I. Both are different. area M.I is normally used when u calculate the bending moments and bending stresses in design of beams and structures. where as mass M.I is used in case of problems related to rotational dynamics. In Mass M.I the mass of the rotating object defenitely plays a role. Its value is calculated by multiplying the mass of individual elements and the square of distance between the element and the axis of rotation. Ie I=Mr^2... Hope its clear now...
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation.

2. How is moment of inertia related to mass?

Moment of inertia is directly proportional to an object's mass. This means that as an object's mass increases, its moment of inertia also increases.

3. Does the shape of an object affect its moment of inertia?

Yes, the shape of an object does affect its moment of inertia. Objects with a larger radius or those that are more spread out have a greater moment of inertia compared to objects with a smaller radius or those that are more compact.

4. How does moment of inertia affect an object's rotational motion?

The moment of inertia affects an object's rotational motion by determining how much torque is required to produce a certain amount of angular acceleration. Objects with a higher moment of inertia require more torque to rotate at the same speed as objects with a lower moment of inertia.

5. Can two objects with the same mass have different moments of inertia?

Yes, two objects with the same mass can have different moments of inertia if their mass is distributed differently. For example, a solid sphere and a hollow sphere with the same mass will have different moments of inertia due to their different distributions of mass.

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