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

Determine the mass moment of inertia of a quarter of an annulus

  • Thread starter jaredogden
  • Start date
  • #1
79
0

Homework Statement


B.1

The quarter ring has mass m and was cut from a thin uniform plate. Knowing that r1 = 1/2r2 determine the mass moment of inertia of the quarter ring with respect to A. axis AA' B. The centroidal axis CC' that is perpendicular to the plane of the quarter ring.

CC' is located possibly where the center of mass is? (See attached file). EDIT: obviously it is the centroid.. the problem says centroidal axis, I'm dumb..

Homework Equations



IAA' = 1/4mr2
ICC' = 1/2mr2

Parallel Axis Theorem
I = I(bar) + md2

The Attempt at a Solution



I originally tried to just use the mass moments of inertia to calculate it. I then realized that the center of mass of the quarter annulus will not be at the origin O in this case so I probably will have to use the parallel axis theorem.

I am really lost on this and I originally calculated
IAA' = (1/16)m(r22 - (1/2)r22)
ICC' = (1/8)m(r22 - (1/2)r22)
 

Attachments

Last edited:

Answers and Replies

  • #2
79
0
I've calculated I(bar)AA' = (1/4)[(1/4)(mr22 - (1/2)mr22)] and simplified this to:
I(bar)AA' = (1/32)mr22

Then adding that to md2 where d = (1/2)r1 → (1/4)r2 from the parallel axis theorem to get
(1/32)mr22 + m(1/4)r22 = (9/32)mr22

The answer given by my professor is (5/16)mr22
Did I make a mistake somewhere or is the provided answer wrong?
 

Related Threads on Determine the mass moment of inertia of a quarter of an annulus

  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
5
Views
16K
Replies
1
Views
3K
Replies
8
Views
10K
Replies
8
Views
47K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
681
  • Last Post
2
Replies
48
Views
15K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
2K
Top