Is my procedure correct to compute this moment of inertia J?

In summary, the moment of inertia J is a physical property that measures an object's resistance to rotational motion and can be calculated using the formula J = ∫r²dm. The terms "moment of inertia" and "mass moment of inertia" are interchangeable and refer to the same property. To ensure correctness, one can check calculations against known values or compare results with a different method. The moment of inertia J is always a positive quantity and cannot be negative.
  • #1
Marvin94
41
0
Looking at the image below, we have the function

[itex]z^2=\frac{r^2}{a} y[/itex]revolving about y-axis. We know that y goes from 0 to "a". We also know the mass of the object (of uniform density). Do you think is my procedure correct? Do you get the same result?

IMG_20150729_183245.jpg
 
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  • #2
I did wrong calculation. The results should be

(2 m r^2) / 3

without "a".
 

1. What is the moment of inertia J?

The moment of inertia J is a physical property that measures an object's resistance to rotational motion. It depends on the mass distribution of the object and the axis of rotation.

2. How do I calculate the moment of inertia J?

The moment of inertia J can be calculated using the formula J = ∫r²dm, where r is the distance from the axis of rotation to the element of mass dm. The integral is taken over the entire object.

3. Is there a difference between moment of inertia and mass moment of inertia?

No, the terms "moment of inertia" and "mass moment of inertia" are often used interchangeably and refer to the same physical property. However, there are other types of moments of inertia, such as area moment of inertia, which are not related to mass.

4. How do I know if my procedure for computing the moment of inertia J is correct?

To ensure the correctness of your procedure, you can check your calculations against known values or compare your results with those obtained using a different method. It is also important to carefully consider all the variables and assumptions involved in your calculation.

5. Can the moment of inertia J be negative?

No, the moment of inertia J is always a positive quantity. It represents the rotational inertia of an object and cannot be negative.

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