Moment of inertia (formula problem)

[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

[/B]
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.

 

[Doc Al]

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.)

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. :)

 

[sseebbeekkk]

Ok, thank you :)

 

[sseebbeekkk]

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

Instead of [1/12ml²+md²]*α

 

[Doc Al]

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.

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

Instead of [1/12ml2+md2]*α

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

 

[sseebbeekkk]

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 ?

 

[Doc Al]

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).

 

[sseebbeekkk]

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