Confusion about moment of inertia

In summary, moment of inertia is a measure of an object's resistance to rotational motion and is often confused with mass or moment of force. It is affected by the distribution of mass and the axis of rotation, and is commonly used in physics and engineering to analyze rotational systems. Understanding the concept of moment of inertia is crucial in accurately predicting the behavior and stability of rotating objects.
  • #1
Hoshiiiiiiiiiiiii
4
0
Member advised to use the formatting template for all homework help requests
When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?
 
Physics news on Phys.org
  • #2
Hoshiiiiiiiiiiiii said:
When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?
In the absence if any other information, it would be about an axis through the mass centre, but that still leaves open more than one possibility. If it is essentially a 2D shape I suggest an axis normal to that.
Please post the whole question, word for word, with any diagrams.
 
  • #3
The question says "Calculate the second moment of area of the T-section given below" with this diagram
KSoA5Q2.jpg

I have found the moment of inertia with respect to both axes correctly, but I'm confused whether I should leave them like that or add them together to get the polar second moment of area.
 

Attachments

  • KSoA5Q2.jpg
    KSoA5Q2.jpg
    5.7 KB · Views: 562
Last edited by a moderator:
  • #4
Hoshiiiiiiiiiiiii said:
The question says "Calculate the second moment of area of the T-section given below" with this diagram https://www.physicsforums.com/attachments/shear-stresses-on-beam-mechanics-of-solids-41-1-jpg.234480/?temp_hash=efb03e1eeffac051d9d9072edf2482c7

I have found the moment of inertia with respect to both axes correctly, but I'm confused whether I should leave them like that or add them together to get the polar second moment of area.
The image us not working for me. Nothing happens when I click the icon.
 
  • #5
haruspex said:
The image us not working for me. Nothing happens when I click the icon.
I edited my reply. I think it's working now.
 
  • #6
Hoshiiiiiiiiiiiii said:
I edited my reply. I think it's working now.
Yes, I see it now.
I stick with my earlier guess: take the axis as being through the mass centre and normal to the plane.
 
  • #7
Thank you so much!
 
  • #8
haruspex said:
take the axis as being through the mass centre and normal to the plane.

Does it simply mean calculating MOI at centriodal axis?
 
  • #9
Benjamin_harsh said:
Does it simply mean calculating MOI at centriodal axis?
AS far as I am aware, a centroidal axis is any axis that passes through the centroid. See e.g. https://www.quora.com/What-is-the-difference-between-Neutral-axis-and-Centroidal-axis.
Also, please do not keep referring to an MoI "at" an axis. An axis is a line. Write MoI about an axis.

For a lamina, a centroidal axis could be within the plane of the lamina, at any angle, or not even within the plane.
A useful theorem is the perpendicular axis theorem. This says that you can find the MoIs about any two such axes at right angles in the plane and add them together to find the MoI about the axis through the centroid and normal to the plane.
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It takes into account an object's mass, shape, and distribution of mass relative to its axis of rotation.

2. How is moment of inertia different from mass?

While mass is a measure of an object's resistance to linear motion, moment of inertia is a measure of its resistance to rotational motion. In other words, mass describes the amount of matter in an object, while moment of inertia describes how that mass is distributed in relation to its axis of rotation.

3. What is the formula for moment of inertia?

The formula for moment of inertia is I = mr², where I represents the moment of inertia, m is the mass of the object, and r is the distance between the object's axis of rotation and the mass. This formula is used for calculating the moment of inertia for a point mass, while more complex formulas are used for objects with a larger or irregular shape.

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 will require more torque to achieve the same angular acceleration as objects with a lower moment of inertia.

5. How can moment of inertia be changed?

The moment of inertia can be changed by altering an object's mass, shape, or distribution of mass. For example, bringing mass closer to the axis of rotation will decrease the moment of inertia, while moving it further away will increase it. Changing an object's shape can also have an impact on its moment of inertia.

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
295
  • Introductory Physics Homework Help
2
Replies
40
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
640
Replies
25
Views
466
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
2
Replies
52
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
933
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
902
Back
Top