Calculation of the moment of inertia

Click For Summary

Discussion Overview

The discussion revolves around the calculation of the moment of inertia, particularly the assumptions involved in treating mass as concentrated at the center of mass when determining its effect on rotational motion. The scope includes theoretical considerations and conceptual clarifications related to physics principles.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant questions the validity of assuming mass is concentrated at the center of mass when calculating moment of inertia, suggesting this assumption may not always hold true.
  • Another participant explains that moment of inertia reflects not only the total mass but also the distribution of that mass relative to the axis of rotation, emphasizing the importance of distance from the axis.
  • A later reply notes the relationship between moment of inertia and statistical concepts like standard deviation, highlighting that similar mathematical principles apply across different contexts.
  • Another participant adds that while the second moment of area is solely dependent on the geometry of a cross-section, the mass moment of inertia is influenced by the actual mass of the object.

Areas of Agreement / Disagreement

Participants express varying perspectives on the assumptions related to the calculation of moment of inertia, indicating that multiple competing views remain without a clear consensus.

Contextual Notes

The discussion does not resolve the assumptions regarding the concentration of mass at the center of mass and its implications for moment of inertia calculations, leaving these points open for further exploration.

Dranzer
Messages
10
Reaction score
0
I was wondering why we can not always assume the mass of a body to be concentrated at the Center of Mass and then multiplying the total mass by the square of the distance from center of mass to the axis,while calculating the moment of inertia of a body.(I found this question in University Physics)

Thank you.
 
Physics news on Phys.org
Hi Dranzer:

The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. Therefore, it encompasses not just how much mass the object has overall, but how far each bit of mass is from the axis. The further out the object's mass is, the more rotational inertia the object has, and the more torque (force* distance from axis of rotation) is required to change its rotation rate.

http://en.wikipedia.org/wiki/Moment_of_inertia
 
Thank you very much.I didn't quite think of that.
 
It's interesting to note that the MI relates to the Standard Deviation of a statistical distribution and also to the strength of a beam. They're all 'second moments'.
Same maths crops up all over the place.
 
An interesting thing to add though, is that the second moment of area only depends one the geometry of the cross section, while the mass moment of inertia also depends on the actual mass.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 49 ·
2
Replies
49
Views
6K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 30 ·
2
Replies
30
Views
5K
  • · Replies 2 ·
Replies
2
Views
1K