Is My Calculation of Moment of Inertia Using the Parallel Axis Theorem Correct?

In summary, the individual was seeking validation for their attempt to solve a problem involving the moment of inertia. Another person confirmed that their solution was correct, but offered a suggestion to simplify the expression. The individual thanked the person for their help and the conversation ended with a suggestion to use the parallel axis theorem in reverse.
  • #1
Romain Nzebele
21
0
Homework Statement
If M=0.50Kg, L=1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.
Relevant Equations
Xcm=total mx/ total m
The picture of the problem and my attempt to solve it are below. Please let me know if my resolution is correct. Thank you in advance.
242976
1557069337351.png
 
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  • #2
Yes, it looks right. Personally, I would have kept ##M## and ##L## until you had a single expression for the MoI. In this case ##3.2ML^2##.
 
  • #3
PeroK said:
Yes, it looks right. Personally, I would have kept ##M## and ##L## until you had a single expression for the MoI. In this case ##3.2ML^2##.
Great, thank you so very much.
 
  • #4
A slightly easier way is to use the parallel axis theorem 'in reverse'.
Find the MoI about the central mass M and subtract (Σm)x2, where x is the displacement to the common mass centre.
 

FAQ: Is My Calculation of Moment of Inertia Using the Parallel Axis Theorem Correct?

What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to rotational motion. It is often referred to as the rotational mass or angular mass of an object.

How is the moment of inertia calculated?

The moment of inertia can be calculated by multiplying the mass of an object by the square of its distance from its axis of rotation. It is represented by the symbol "I" and has units of kg·m² in the SI system.

What is the difference between moment of inertia and mass?

Moment of inertia and mass are two distinct concepts. Mass is a measure of the amount of matter in an object, while moment of inertia is a measure of an object's resistance to rotational motion. They are related, but not interchangeable, as an object's mass can affect its moment of inertia.

How does the distribution of mass affect an object's moment of inertia?

The distribution of mass in an object can greatly affect its moment of inertia. Objects with more mass concentrated closer to the axis of rotation will have a lower moment of inertia, while objects with more mass distributed farther from the axis will have a higher moment of inertia.

Why is the concept of moment of inertia important in physics?

The moment of inertia is an important concept in physics because it plays a crucial role in rotational motion and can help predict an object's behavior when subjected to rotational forces. It is also used in engineering and design to optimize the performance and stability of rotating objects.

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