Moment of Inertia Calculation for Conic Disc with Hole in Center

Click For Summary
SUMMARY

The discussion focuses on calculating the moment of inertia for a conic disc with a central hole. The approach involves treating the disc as a series of concentric rings, where the contribution of each mass element to the moment of inertia is expressed as r² dm. Participants emphasize the importance of defining dm in terms of the radius (r) and the density of the material, followed by setting up the appropriate integral for calculation.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Knowledge of calculus, specifically integration techniques
  • Familiarity with density and mass distribution
  • Basic principles of physics related to rotational motion
NEXT STEPS
  • Study the derivation of moment of inertia for various geometric shapes
  • Learn about integration techniques for calculating areas and volumes
  • Explore applications of moment of inertia in engineering and physics
  • Investigate the properties of conic sections in relation to mass distribution
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying mechanics, as well as educators and anyone interested in advanced calculations related to rotational dynamics.

CBrandi
Messages
1
Reaction score
0
Hi everybody.
I'm a newbie here.
I'm a Physics student at University of São Paulo in Brazil (I'm in 1st year) and find this forum was a very nice surprise for me. I think this is the best thing about Physics in all web and I would like give all of you my congratulations.
Well, my doubt is about Moment of Inertia.
I need calculate the moment of inertia for a conic disc with a hole in the center according the figure below. I made several searches on Internet and didn't find nothing about this.
The diametral section of the ring is like following:
http://img178.imageshack.us/img178/7999/discocnico013ai.jpg
Thank you very much.
 
Last edited by a moderator:
Physics news on Phys.org
set up the integral

Realize that the contribution of a given mass element to the moment of inertia is [itex]r^2 dm[/itex]. Hint: Treat the object as composed of a set of concentric rings. Write "dm" for these rings as a function of r and the density. Integrate!
 

Similar threads

  • · Replies 40 ·
2
Replies
40
Views
7K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
13
Views
4K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
1
Views
1K
Replies
16
Views
3K
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
7K