Moment of inertia of a cross system

In summary: It states that the moment of inertia of a rod about an axis perpendicular to the page and passing through point O is equal to the sum of the moments of inertia about the other two perpendicular axes. This is what you calculated.
  • #1
Rheegeaux
6
0

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 :)
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  • #2
Show the details of your attempt.
 
  • #3
gneill said:
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
 
  • #4
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?
 
  • #5
gneill said:
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 :)
 
  • #6
Check your course text or on the web for "Parallel axis theorem".
 

What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion and depends on the mass and distribution of the object's mass.

How is moment of inertia calculated for a cross system?

The moment of inertia for a cross system can be calculated by summing the moments of inertia for each individual component. The moment of inertia for a rectangular cross section can be calculated using the formula I = (1/12) * m * (h^2 + b^2), where m is the mass of the object and h and b are the height and width of the cross section, respectively.

What factors affect the moment of inertia of a cross system?

The moment of inertia of a cross system is affected by the mass, shape, and distribution of the object's mass. Objects with more mass or a larger distribution of mass have a higher moment of inertia, while objects with less mass or a smaller distribution of mass have a lower moment of inertia.

How does moment of inertia impact rotational motion?

Moment of inertia plays a critical role in rotational motion. A higher moment of inertia means an object will be more resistant to changes in its rotational motion, while a lower moment of inertia means the object will be easier to rotate. This can affect the speed and stability of an object's rotation.

What are some real-world applications of moment of inertia of a cross system?

Moment of inertia is important in many engineering and physics applications, such as designing and analyzing the stability of structures and machines, understanding the behavior of rotating objects, and calculating the energy and power required for rotational motion.

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