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zenterix
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- Homework Statement
- (Apostol, Vol II, 2nd Ed., Chapter. 12.10, Problem 10)
A homogenous paper rectange of base and altitude is rolled to form a circular cylindrical surface of radius . Calculate the moment of inertia of about an axis through a diameter of the circular base.
- Relevant Equations
Here is the homogenous paper rectangle
And if we roll it we get a cylinder with base radius .
It is not clear to me what "an axis through a diameter of the circular base means".
Let's imagine such as axis is in the following figure
Then we have
where I have used a mass density of for the cylindrical surface.
Now, technically, if we were to use the following axis instead
then it also "passes through" a diameter of the circular base. In this case we have
Neither one of these calculations matches the answer at the end of the book, which is .
What am I doing wrong here?
And if we roll it we get a cylinder with base radius
It is not clear to me what "an axis through a diameter of the circular base means".
Let's imagine such as axis is
Then we have
where I have used a mass density of
Now, technically, if we were to use the following axis instead
then it also "passes through" a diameter of the circular base. In this case we have
Neither one of these calculations matches the answer at the end of the book, which is
What am I doing wrong here?