Finding the moment of inertia for a specific figure (illustrated)

In summary, the conversation discusses finding the moment of inertia for a given figure with known lengths. The solution involves using the fraction h/2 to represent half of the figure and taking into account the symmetrical bottom half by multiplying the entire integral by 2. The use of similar triangles is mentioned to explain the fraction.
  • #1
PhyIsOhSoHard
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Homework Statement


http://img577.imageshack.us/img577/2069/inertia.gif

The following figure with these known lengths are given. I need to find the moment of inertia.

Homework Equations


According to my book's facit, this is the solution:
http://img845.imageshack.us/img845/6725/inertiaformula.png

The Attempt at a Solution


This is what I understand so far...
The fraction h/2 refers to half the figure (when cut from horizontal). So you start from the middle of the figure, and then move up to the end in which case you have traveled the vertical length h/2. Then by multiplying the entire integral with 2, you take the bottom half of the figure into account as well (since it's symmetrical).

I have no idea about the fraction. I've tried, but I have no idea how they came up with that. All I know is that "y" is the vertical axis for the figure...
 
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  • #2
Welcome to PF!

Hi PhyIsOhSoHard! Welcome to PF! :smile:
PhyIsOhSoHard said:
I have no idea about the fraction. I've tried, but I have no idea how they came up with that. All I know is that "y" is the vertical axis for the figure...

it's similar triangles …

you want the base of the smaller triangle, and you know that the base of the larger triangle is b :wink:
 

1. How do you calculate the moment of inertia for a specific figure?

The moment of inertia for a specific figure can be calculated by using the formula I = ∫r²dm, where I is the moment of inertia, r is the distance from the axis of rotation, and dm is the differential mass of the figure.

2. What is the significance of finding the moment of inertia for a specific figure?

Finding the moment of inertia for a specific figure is important in understanding the distribution of mass in an object and how it will respond to rotational motion.

3. Can the moment of inertia be negative?

No, the moment of inertia is always a positive value as it represents the resistance of an object to changes in its rotational motion.

4. How does the shape of a figure affect its moment of inertia?

The moment of inertia is directly influenced by the shape of a figure. Objects with more mass located farther from the axis of rotation will have a greater moment of inertia, while objects with more mass located closer to the axis will have a smaller moment of inertia.

5. What are some practical applications of finding the moment of inertia for a specific figure?

The moment of inertia is used in various fields, such as engineering, physics, and biomechanics. It is essential in designing and analyzing the stability and motion of rotating objects, such as wheels, gears, and pendulums.

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