Why do different origins result in different principal moments of inertia?

Click For Summary
SUMMARY

The discussion focuses on the differences in principal moments of inertia calculated from different origins for a system of four equal masses positioned at the corners of a square with side length b. When using one corner as the origin, the principal moments of inertia are calculated as Ixx=mb², Iyy=3mb², and Izz=4mb². In contrast, when the center of mass is used as the origin, the values change to Ixx=mb², Iyy=mb², and Izz=2mb². The key takeaway is that while the values of the principal moments of inertia vary with the choice of origin, the directions of the principal axes remain consistent.

PREREQUISITES
  • Understanding of inertia tensors and their diagonalization
  • Familiarity with the concept of principal moments of inertia
  • Basic knowledge of mass distribution in physics
  • Ability to solve secular equations in mechanics
NEXT STEPS
  • Study the derivation of the inertia tensor for various mass distributions
  • Learn about the parallel axis theorem and its application in calculating moments of inertia
  • Explore the implications of principal axes in rigid body dynamics
  • Investigate the relationship between mass distribution and rotational motion
USEFUL FOR

Students and professionals in physics, particularly those studying mechanics and dynamics, as well as anyone interested in understanding the effects of mass distribution on rotational properties of rigid bodies.

Geocentric
Messages
15
Reaction score
0

Homework Statement


When I try finding the principal moments of inertia with respect to different origins for any arbitrary configuration(assuming that the inertia tensor is diagonalized), I end up getting different values. Intuitively, this is quite acceptable because the mass distribution is different with respect to axes corresponding to different origins. But in both the cases, the directions of principal axes are the same which is what really matter. I would like to have the thoughts of you guys as well on the statements I have made.


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
Sorry, but I don't understand exactly what your question is? And does this relate to a particular homework-type problem? (If not, perhaps someone should ask a mentor to move it to one of the physics discussion forums)
 
Let me be more specific. Consider 4 equal masses at the 4 corners of a square of side b. First I took one of the corners as the origin and found the principal moments of inertia to be Ixx=mb^2, Iyy=3mb^2, Izz=4mb^2 after solving the secular equation. Again, I found the principal moments of inertia but now with respect to the center of mass as origin as Ixx=mb^2, Iyy=mb^2, Izz=2mb^2. Now my question is, why do I get different values of principal moments of inertia?
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 3 ·
Replies
3
Views
8K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 6 ·
Replies
6
Views
12K
  • · Replies 3 ·
Replies
3
Views
3K