Rotational Inertia (Moment of Inertia) of a Rod

  • Thread starter tseryan
  • Start date
  • #1
tseryan
19
1

Homework Statement


A very light (meaning don't consider mass of the rod) rod is placed along the x axis. It has a mass m1=2.0kg at x=0, a mass m2=1.50kg at x=50cm, and a mass m3=3.0kg at x=100cm.

Find the moment of inertia of the system about a pivot point at x=0.


Homework Equations



I=(1/3)M(L^2) -- Parallel Axis Theorem

I= integral of[(r^2)dm]?

The Attempt at a Solution



Because the mass of the rod does not matter, I'm thinking of finding the center of mass between the three masses and treating that as one whole mass at a certain point x. Does that idea make any sense? Any help would be greatly appreciated!
 

Answers and Replies

  • #2
Doc Al
Mentor
45,447
1,907
That would be a bad idea. The rotational properties depend on the distribution of mass, not just the center of mass. Hint: What's the rotational inertia of a point mass about some axis?
 
  • #3
tseryan
19
1
It is I=MR^2. If I find the sum of the point masses of inertia I get the moment of inertia? Does it matter that it's on a rod?
 
  • #4
Doc Al
Mentor
45,447
1,907
It is I=MR^2.
Right.
If I find the sum of the point masses of inertia I get the moment of inertia?
Absolutely.
Does it matter that it's on a rod?
Nope. (You need something to connect the masses as a rigid structure.)
 
  • #5
tseryan
19
1
Got it! Thanks Doc Al! Now I don't understand why there is a Parallel Axis Theorem for a rod with the equation I=(1/3)M(L^2). What would that be used for?
 
  • #6
Doc Al
Mentor
45,447
1,907
Not sure I understand your question. The parallel axis theorem applies to any object, not just a rod.

Starting with the rotational inertia of a rod about its center of mass (what's the formula for that?), the parallel axis theorem will allow you to find the rotational inertia of the rod about any other parallel axis--including about one end, which is what (1/3)M(L^2) is for. (Try it--it's easy.)
 

Suggested for: Rotational Inertia (Moment of Inertia) of a Rod

  • Last Post
Replies
3
Views
481
Replies
13
Views
416
Replies
3
Views
243
Replies
21
Views
365
Replies
5
Views
575
  • Last Post
Replies
3
Views
426
Replies
8
Views
629
Replies
4
Views
453
  • Last Post
Replies
11
Views
656
Top