# Moment of inertia (formula problem)

• sseebbeekkk
In summary, the author uses two different values of rotational inertia for the same slender rod in order to calculate the moment of inertia.
sseebbeekkk
1. Material

2. Questions:

a) (pink) Why does the author use two different values of inertia for the same slender rod ?

## The Attempt at a Solution

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a) I could assume that 1/3 is holding it at the end and 1/12 is holding it in the center.
But it's not interchangeable because if I chose 1/3 instead of 1/12 in the example (17.10) I would get totally different final result.

sseebbeekkk said:
a) I could assume that 1/3 is holding it at the end and 1/12 is holding it in the center.
They are the rotational inertias about the end and about the center, respectively. It is up to you to figure out which is the most useful point for calculating moments in any particular problem. (Sometimes it doesn't matter.)

sseebbeekkk said:
But it's not interchangeable because if I chose 1/3 instead of 1/12 in the example (17.10) I would get totally different final result.
Realize that 17.10 uses both values of rotational inertia. :)

Ok, thank you :)

Ok I have realized that I don't understand it fully (I miss something basic probably)

According to this example we should calculate the moment of inertia using formula I=1/12ml2+md2

So why did the author in 17.10 use simply [1/12ml2]*α

sseebbeekkk said:
According to this example we should calculate the moment of inertia using formula I=1/12ml2+md2
Only because you want the moment of inertia about point O.

sseebbeekkk said:
So why did the author in 17.10 use simply [1/12ml2]*α

Because the author was calculating the moment of inertia about the center of mass, not the end of the rod.

Ok, finally I understand it (hope so)

I can choose I=1/12ml2 = in that case (17.10) 1/12*20*32=15
or I=1/3ml2 = (center at 1.5) 1/3*20*1,52=15

It works EDIT: but if that what I have just written is true, I have got the following question:

Why did the author write in 17.12 (1/3ml2) instead of 1/3m * (l/2)2 ?

Last edited:
sseebbeekkk said:
Ok, finally I understand it (hope so)

I can choose I=1/12ml2 = in that case (17.10) 1/12*20*32=15
or I=1/3ml2 = (center at 1.5) 1/3*20*1,52=15
Don't do that!

In both formulas, the "l" stands for the length of the rod. It's the same value in both formulas. The moment of inertia about one end (the 1/3 formula) is different from the moment of inertia about the center (the 1/12 formula).

That was very concise and clear.
Thank you :-)

## 1. What is the formula for moment of inertia?

The formula for moment of inertia is I = mr², where I is moment of inertia, m is mass, and r is the distance from the axis of rotation to the mass.

## 2. How do you calculate moment of inertia for a complex object?

Moment of inertia for a complex object can be calculated by breaking it down into smaller, simpler shapes and using the formula I = mr² for each individual shape. Then, the individual moments of inertia can be added together to get the total moment of inertia for the object.

## 3. What is the difference between moment of inertia and mass moment of inertia?

Moment of inertia is a measure of an object's resistance to change in rotational motion, while mass moment of inertia is a measure of an object's resistance to change in angular velocity. Mass moment of inertia takes into account not only the mass of an object, but also how that mass is distributed around the axis of rotation.

## 4. How does the moment of inertia affect an object's rotational motion?

The moment of inertia determines how difficult it is to change an object's rotational motion. Objects with a larger moment of inertia will be more resistant to changes in rotational motion, while objects with a smaller moment of inertia will be easier to rotate.

## 5. Can the moment of inertia of an object change?

Yes, the moment of inertia of an object can change if the mass or distribution of mass around the axis of rotation changes. For example, if an object's mass is moved further away from the axis of rotation, the moment of inertia will increase.

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