How to calculate the moment of inertia of a system with multiple bodies?

In summary, the conversation involves calculating the moment of inertia in the OO' axis for a figure with 5 separate bodies. The relevant equations for this calculation are provided, including a formula for changing the axis of moment of inertia from the center of mass to a parallel axis. The person attempting the solution is unsure if their method of finding the total moment of inertia by separately calculating the moments of inertia for each body and then adding them together is correct, and is asking for confirmation by providing the 5 separate moments of inertia.
  • #1
CollinsArg
51
2

Homework Statement


Calculate the moment of inertia in the OO' axis of the following figure (image attached).

Homework Equations


The relevant equations are in the image,
except: I = Icm + m.h2 (formula of moment of inertia to change the axis from the centre of mass to a parallel axis).

The Attempt at a Solution


I tried to find the moment of inertia of each figure separately/individually depending of the OO' axis by the formula give in "relevant equations" then sum all up to find the total moment of inertial of the system. Is this right? I'm not sure how to evidence this is correct
 

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  • #2
You need to show more work before one can tell whether your answer is correct. Your method is correct. You have 5 bodies, you need to calculate the moment of inertia about axis OO' for each one separately then add all the results. If you want someone to check your work, please provide the 5 separate moments of inertia, not just the final answer.
 
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FAQ: How to calculate the moment of inertia of a system with multiple bodies?

1. What is moment of inertia of a body?

Moment of inertia is a physical property of a body that describes its resistance to rotational motion. It is a measure of how much force is needed to change the body's rotational speed.

2. What factors affect the moment of inertia of a body?

The moment of inertia of a body is affected by its mass, shape, and distribution of mass around its rotation axis. The farther the mass is from the axis of rotation, the larger the moment of inertia will be.

3. How is moment of inertia different from mass?

Moment of inertia is often compared to mass, but they are not the same. Mass is a measure of an object's resistance to linear motion, while moment of inertia is a measure of its resistance to rotational motion.

4. How is moment of inertia calculated?

The moment of inertia of a body can be calculated using the formula I = ∫ r² dm, where r is the distance from the rotation axis to the element of mass, and dm is the mass of that element. This integral is often simplified using mathematical techniques.

5. Why is moment of inertia important in physics?

Moment of inertia is important in physics because it plays a crucial role in determining how objects move and interact with each other in rotational motion. It is also used in various engineering applications, such as designing structures and machines with optimal stability and efficiency.

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