Why is Ix/Iy used instead of Iz for the mass moment of inertia?

In summary, mass moment of inertia, also known as rotational inertia, is a measure of how much an object's mass is distributed from its axis of rotation. It is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation and is important in understanding rotational motion. There is a slight difference between mass moment of inertia and moment of inertia, with the former specifically referring to rotational inertia. A higher mass moment of inertia leads to greater stability in objects.
  • #1
princejan7
93
0

Homework Statement




for the mass moment of inertia, why did they use Ix/Iy and not Iz?

Homework Equations



Ix=Iy= 1/12 m (3(r^2) + (h^2))
Iz= 1/2 m (r^2)

The Attempt at a Solution

 

Attachments

  • Untitled.png
    Untitled.png
    32.7 KB · Views: 443
Physics news on Phys.org
  • #2
The axis of rotation is in the direction of the j-axis or vertical axis. The test tube isn't rotating about it's own centroidal axis.
 

What is mass moment of inertia?

The mass moment of inertia, also known as rotational inertia, is a physical property of an object that describes its resistance to rotational motion. It is a measure of how much an object's mass is distributed from its axis of rotation.

How is mass moment of inertia calculated?

The mass moment of inertia is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. It is also affected by the shape and distribution of the object's mass.

Why is mass moment of inertia important?

Mass moment of inertia is important because it determines how easily an object can rotate or resist rotational motion. It is essential in understanding the behavior of objects in rotational motion, such as spinning tops, wheels, and even planets.

What is the difference between mass moment of inertia and moment of inertia?

Mass moment of inertia and moment of inertia are often used interchangeably, but they are slightly different concepts. Mass moment of inertia specifically refers to the rotational inertia of an object, while moment of inertia can refer to both rotational and translational inertia.

How does mass moment of inertia affect an object's stability?

The higher the mass moment of inertia of an object, the more difficult it is to change its rotational motion. This means that objects with a higher mass moment of inertia are generally more stable and less likely to tip over or rotate easily.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
831
  • Introductory Physics Homework Help
Replies
2
Views
527
  • Introductory Physics Homework Help
Replies
11
Views
237
  • Introductory Physics Homework Help
Replies
3
Views
788
  • Introductory Physics Homework Help
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
28
Views
461
  • Introductory Physics Homework Help
Replies
11
Views
1K
Replies
25
Views
344
  • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
Back
Top