Rotated Section - Moment of Inertia

Click For Summary

Discussion Overview

The discussion revolves around the calculation of the moment of inertia for a 2D area that has been rotated about an axis. Participants explore whether there is a specific formula to determine the new moments of inertia after the area has been rotated, as opposed to rotating the axes themselves.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Eduardo inquires about the existence of a formula to calculate the moment of inertia of a rotated section, specifically after rotating a 2D area around the origin by a certain angle.
  • Some participants seek clarification on Eduardo's question, asking for additional explanation or diagrams to better understand the concept.
  • Eduardo explains that he has known values for the moments of inertia (Ix, Iy, Pxy) and is looking for a way to calculate the new values after the area has been rotated, without changing the axes.
  • One participant suggests that rotating the area can be viewed as equivalent to rotating the axes in the opposite direction, proposing that the same formulas could be used with a negative rotation angle.

Areas of Agreement / Disagreement

There is no clear consensus on the approach to take for calculating the moment of inertia after the area has been rotated, as participants have differing interpretations of the problem and its solution.

Contextual Notes

Participants have not reached an agreement on the method to calculate the new moments of inertia, and there may be assumptions about the definitions and relationships between the rotation of the area and the axes that remain unresolved.

eriveraa80
Messages
2
Reaction score
0
Hi everybody:

I can see that there are formulas to calculate the moment of inertia of a 2D Area (Second moment of area) here: http://en.wikipedia.org/wiki/Second_moment_of_area"

In the same link, there is a formula to calculate the Inertia moments about a ROTATED AXIS (Axis Rotation). But, is there a formula to calculate the Inertia moments of a ROTATED SECTION (rotated area) ??

Thanks in advance.
Eduardo
 
Last edited by a moderator:
Physics news on Phys.org
Not sure what you mean. Can you provide additional explanation by means of a diagram or other hand waving?
 
Ok, i will explain a little bit:

1. You have a 2D Area in a XY axis. You can calculate the Moments of Inertia Ix, Iy, Pxy.
2. You rotate the 2D Area around the origin, with a tetha angle.
3. So, known Ix, Iy, Pxy and tetha: Is there a formula so i can calculate the new Ix, Iy, Pxy around the same axis?

In wikipedia, you can see that there is a way of calculating the Ix', Iy' and Pxy' around the rotated axis, but that is not what i want, because i am not rotating Axis. I am rotating only the 2D Area and i want calculate Ix, Iy, Pxy in the same axis based on the previously Ix, Iy, Pxy calculated.

Any ideas?
 
Hello Eduardo, you should not create duplicate posts in different sections.

Can you see that rotating the area in one direction is the same thing as rotating the axes in the other direction?

So you should use the same formulae, but the rotation angle is negative.
 

Similar threads

Undergrad Resolve moment of inertia at an angle
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Moment of Inertia about an axis and Torque about a point
  • · Replies 5 ·
Replies
5
Views
3K
High School Moment of Inertia of Rectangles
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Axial angular momentum calculation
  • · Replies 30 ·
2
Replies
30
Views
5K
Undergrad Why Do Different Objects Share Similar Moments of Inertia?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How find moment of inertia for car in turn?
  • · Replies 49 ·
2
Replies
49
Views
6K
Undergrad How Is Power Calculated in a Rotating System with Variable Speed?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Inertia of body moving about two distinct parallel axes
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Moment of inertia of human body with limbs at an angle
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Effects of External Torques on the Angular Momentum of Asymmetric Bodies
  • · Replies 3 ·
Replies
3
Views
2K