• Support PF! Buy your school textbooks, materials and every day products Here!

Moment of inertia of a non uniform disc

  • Thread starter Rnm
  • Start date
  • #1
Rnm
4
1

Homework Statement


A non uniform disc of radius R has a mass of M. Its centre of gravity is located at a distance x from the centre. Find the moment of inertia of mass (moi) around the axis perpendicular to the surface passinf through the centre of gravity.

Homework Equations


Parallel axis theorem
Ioo = Igg + m[r^2]

Ioo = moi around axis required
Igg = moi around axis through centre of gravity
m = mass of the object
r = distance between the 2 axises(?dont know the plural)

Moi around the centre of a uniform disc
1/2m[r^2]

The Attempt at a Solution

[/B]
I assumed that since Ioo = 1/2M[R^2]
Then using parallel axis theorem i took
Igg =1/2M[R^2] - M[x^2]
The problem is you can get a negative answer for Igg for certain x(>R/root2). So i think im wrong some where in my assumptions. Can someone please clarify
 
Last edited by a moderator:
  • Like
Likes berkeman

Answers and Replies

  • #2
Doc Al
Mentor
44,940
1,201
I assumed that since Ioo = 1/2M[R^2]
Why would you assume that? (That's the MOI of a uniform disk through its center.)

Have you posted the full problem? I don't see sufficient information to solve for anything.
 
  • #3
CWatters
Science Advisor
Homework Helper
Gold Member
10,529
2,295
+1

Looks like something is missing.
 
  • #4
Rnm
4
1
Why would you assume that? (That's the MOI of a uniform disk through its center.)

Have you posted the full problem? I don't see sufficient information to solve for anything.
This is the first part of the question.
The 2nd part involves placing this disk on a horizontal table at rest and letting go. The disk starts to roll (with no slipping) along the table . I need to use the answers i obtained in the first part to find the vertical and horizontal components of the reaction force on the disk by the table

I wrote 3 equations for this with newtons 2nd law in the vertical and horizontal directions and the 2nd law of rotation in the direction of the angular acceleration (a)
I cant figure out how to write the last equation without using Igg. (Since it is stated to use the previous result).
 
  • #5
CWatters
Science Advisor
Homework Helper
Gold Member
10,529
2,295
Are you sure the problem says it's a NONuniform disc not a uniform disc?

Consider the case when x=0. There are lots of ways that such a disc can be "nonuniform" and the moment of inertia will be different in each case. For example the disc could be thicker in the middle or thicker at the edge. That would change the moment of inertia while keeping x unchanged. You couldn't calculate the moment of inertia without knowing the mass distribution.
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,463
5,410
Are you sure the problem says it's a NONuniform disc not a uniform disc?
Its centre of gravity is located at a distance x from the centre
 
  • Like
Likes CWatters
  • #7
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,463
5,410
A non uniform disc of radius R has a mass of M. Its centre of gravity is located at a distance x from the centre. Find the moment of inertia of mass (moi) around the axis perpendicular to the surface passinf through the centre of gravity.
As others have posted, this is not nearly enough information. As an example, consider a uniform disc mass m with a point mass M-m stuck on at distance y from the disc's centre. The moment of inertia about the mass centre of the combination is mr2/2+Mmx2/(M-m).

Edit: No, that can't be right... something nasty anyway.
 
Last edited:
  • #8
Rnm
4
1
No other data is given in the question. I double checked. I suppose the question is incomplete then? But if so what would be missing in the question?
 
  • #9
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,463
5,410
what would be missing in the question?
I cannot think of one simple extra piece of information that would allow you to find the moment.
I suggest you just write it as J and proceed to the second part of the question.

Edit: I found an old question exactly the same except that it did not expect you to determine the moment of inertia. It just said it is I, and asked about the oscillation. This suggests to me that asking for the moment of inertia was just a mistake.
 
Last edited:
  • Like
Likes CWatters
  • #10
Rnm
4
1
I suggest you just write it as J and proceed to the second part of the question.
Will do. Ill try to find the missing information about the question. Thanks for helping me out.
 

Related Threads on Moment of inertia of a non uniform disc

  • Last Post
Replies
7
Views
4K
Replies
10
Views
13K
Replies
1
Views
9K
Replies
8
Views
5K
  • Last Post
Replies
1
Views
1K
Replies
7
Views
12K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
6K
Top