Moment of inertia of a cross system

[Rheegeaux]

Homework Statement

Two identical rods, each with mass 5.00 kg and length 2.00m are welded as shown
in the figure. If the moment of inertia of a rod about an axis passing through its center is
Icm = 1/12ML2, what is the moment of inertia of the system of rods about an axis perpendicular
to the page and passing through point O?

Homework Equations

1/12ML^2, MR^2

The Attempt at a Solution

I tried to get the sum of the two moments of inertia but it gave me none of the choices. Please help I need to understand this for a big test tomorrow cheers :)

 

[gneill]

Show the details of your attempt.

 

[Rheegeaux]

Show the details of your attempt.

1/12ML^2 + 2/3*M(2/3L)^2 + 1/12 ML^2 = and I get 6.29.
Please explain the question to me because I don't seem to grasp it yet even make a proper solution. thanks

 

[gneill]

There are two rods. At first treat them separately. Each one is rotating about the point O which is not their center of mass. Find the moment of inertia of each rod about point O. What theorem will you apply?

 

[Rheegeaux]

There are two rods. At first treat them separately. Each one is rotating about the point O which is not their center of mass. Find the moment of inertia of each rod about point O. What theorem will you apply?

I got it! But could you exlpain why that is the answer? What I did is I treated the first one as a point particle and applied the parallel axis theorem, then what I did is I added that to the moment of inertia of a rod hence I got 17.222. I got it but I want to understand how and why I got it, could you please explain? Your help is very much appreciated! Thanks :)

 

[gneill]

Check your course text or on the web for "Parallel axis theorem".