Moment of inertia (disk with off center hole)

Click For Summary
SUMMARY

The discussion focuses on calculating the moment of inertia (MoI) for a disk with an off-center circular hole. The user initially considers subtracting the MoI of the hole from that of the disk but realizes the need for the parallel axis theorem to account for the hole's offset. To find the mass of the missing hole, a method is suggested: dividing the disk's mass by its area to determine density, then applying this density to the area of the hole. This approach allows for accurate MoI calculations necessary for further analysis.

PREREQUISITES
  • Understanding of moment of inertia (MoI) concepts
  • Familiarity with the parallel axis theorem
  • Basic knowledge of density calculations
  • Ability to apply geometric principles to physical problems
NEXT STEPS
  • Study the parallel axis theorem in detail
  • Learn how to calculate the moment of inertia for various shapes
  • Explore density calculations for irregular shapes
  • Investigate applications of moment of inertia in rotational dynamics
USEFUL FOR

Engineering students, mechanical engineers, and anyone involved in physics or mechanical design who needs to calculate the moment of inertia for complex shapes.

Imperitor
Messages
19
Reaction score
0
I have a disk with some thickness to it and I need its moment of inertia.
So this is the formula with r1=0
37f7b2c6aaaf32e1972af5e228064928.png


Now there is a "circular hole of diameter 'd' at a distance of 'r' from the geometric center of the disk." So I'm thinking that I should subtract the MoI of the hole from the disk. Here is a picture if you need it.

http://img99.imageshack.us/img99/782/50817033.jpg

I could use the same MoI equation as I did for the disk on the hole but that doesn't account for the hole being off centered. Any ideas??

I need to eventually equate this to a small mass rotating around a center point, so if there is a more direct approach please tell me. Thanks in advance for the help.
 
Last edited by a moderator:
Physics news on Phys.org
Welcome to PF!

Hi Imperitor ! Welcome to PF! :smile:
Imperitor said:
I could use the same MoI equation as I did for the disk

That's right! :smile:

And then use the parallel axis theorem to find the moment of inertia about an axis not through the centre of mass. :wink:
 
Thanks. I really should have known that...

I'm really enjoying this forum. It's a great resource for an engineering student.
 
Wait a minute... hit another snag. To use that theorem I need to know what the mass of the missing hole is. I only know the mass of the disk as is (with the hole in it). Also the first formula I gave could only be used if I knew what the mass of the disk was with the hole filled in. This is driving me nuts. I can't even start working on the question I'm doing without getting this MoI.
 
just got up… :zzz:
Imperitor said:
Wait a minute... hit another snag. To use that theorem I need to know what the mass of the missing hole is. I only know the mass of the disk as is (with the hole in it). Also the first formula I gave could only be used if I knew what the mass of the disk was with the hole filled in. This is driving me nuts. I can't even start working on the question I'm doing without getting this MoI.

Easy-peasy …

divide the given mass by the area, to give you the density :wink: …

then multiply by each area separately! :smile:
 
  • Like
Likes   Reactions: harmyder

Similar threads

Moment of inertia of a disk about an axis not passing through its CoM
  • · Replies 11 ·
Replies
11
Views
3K
What is the "r" in the moment of inertia?
  • · Replies 13 ·
Replies
13
Views
3K
Moment of inertia about center of mass with four holes?
  • · Replies 9 ·
Replies
9
Views
7K
Find the moment of inertia of this disk
  • · Replies 2 ·
Replies
2
Views
5K
Moment of Inertia of an inclined disk
  • · Replies 27 ·
Replies
27
Views
5K
Moment of Inertia of a Spinning Record with a Hole in Center
  • · Replies 13 ·
Replies
13
Views
4K
Rotational Inertia: Hoop vs Disk
  • · Replies 19 ·
Replies
19
Views
4K
How Do You Calculate the Moment of Inertia for a Disk with a Central Hole?
  • · Replies 2 ·
Replies
2
Views
4K
Moment of Inertia with pulley and two masses on a string (iWTSE.org)
  • · Replies 8 ·
Replies
8
Views
14K
Determining $L_{o}$: Finding Angular Momentum of System
  • · Replies 45 ·
2
Replies
45
Views
4K