# Moment of inertia for composite objects

1. Dec 8, 2015

### vetgirl1990

1. The problem statement, all variables and given/known data
Find the moment of inertia of these composite objects.

I've attached two different composite objects; each rod has length L and mass M.

2. Relevant equations
I = Icm + MD2
Long thin rod with rotation axis through centre: Icm = 1/12ML2
Long thin rod with rotation axis through end: Icm = 1/3ML2

3. The attempt at a solution
(a) For the image on the left:
I first found the total inertia of the objects: Icm total = 1/12ML2
Then applied the Parallel Axis Theorem, because the composite object is rotating parallel to the actual axis of rotation: I = 5/12ML2 + 2MD2 (where D is the distance between the object's centre of mass and axis of rotation).
Feedback on this?

(b) For the image on the right:
Since one of the rods are going through the axis of rotation, I don't think I need to apply the Parallel Axis Theorem... So I just found the total inertia for both objects based on where their axis of rotation is.

I = ICM axis through centre + ICM axis through end
= 1/12ML2 + 1/3M(L/2)2
= 1/12ML2 + 1/3ML2/4
= 1/6 ML2

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2. Dec 8, 2015

### Staff: Mentor

Can you give some more details about your determination of the $I_{cm}$ for the first image? I don't see how it turns out to be the same as that of a single rod about its center.

3. Dec 9, 2015

### J Hann

You shouldn't need to use the parallel axis theorem for either situation.
For part (b), aren't all points on the vertical thin rod at a distance of L/2 from the axis of rotation;
or in other words where is the center of mass of the vertical rod in part (b)?