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

Moment of inertia of a door?

  • #1
101
0

Homework Statement


A uniform, thin, solid door has height 2.2 m, width .87m and mass 23kg. Find the moment of inertia for rotation on its hinges.

2. Homework Equations

I=∫x^2dm

The Attempt at a Solution


[/B]The way I set it up was that I made into strips of length H (height) and width dr. dm=λHdr, where λ is mass over the length, H. But when I do the integral ∫r^2λHdr from 0 to r, I end up with ⅓mr^3, but it should be ⅓mr^2. Is lambda supposed to m/rH? If so, can someone explain why please?
 

Answers and Replies

  • #2
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,817
6,625
You can check this, in order for dm to be a mass, ##\lambda## must have dimensions of mass/length^2. It is the mass density per unit area of door.
 
  • #3
101
0
You can check this, in order for dm to be a mass, ##\lambda## must have dimensions of mass/length^2. It is the mass density per unit area of door.
Oh, well that makes sense, thank you. Sometimes I feel like it's the simplest things that I get stuck on.
 

Related Threads on Moment of inertia of a door?

  • Last Post
Replies
5
Views
5K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
7
Views
51K
  • Last Post
Replies
3
Views
25K
  • Last Post
Replies
1
Views
805
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
1
Views
2K
Replies
2
Views
2K
Replies
9
Views
9K
Top