# Stability and moment of inertia

• Jason03
In summary, the problem involves calculating the least moment of inertia using a formula that requires the base and height of a rectangle, which the speaker has determined to be 4 feet and 2 feet respectively. They clarify that this moment of inertia is for the minor axis, and that the major axis moment of inertia would be calculated differently if the rectangle were rotated.

#### Jason03

The problem and my work is below...I believe I got the problem to work out. The only question I had was if I found the LEAST moment of inertia which is what's needed for the formula at the end of my calculations. What exactly is meant by the least moment of inertia?

http://i674.photobucket.com/albums/vv106/jason03_2009/prob7-1.jpg [Broken]

http://i674.photobucket.com/albums/vv106/jason03_2009/prob7-2.jpg [Broken]

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Jason03 said:
The problem and my work is below...I believe I got the problem to work out. The only question I had was if I found the LEAST moment of inertia which is what's needed for the formula at the end of my calculations. What exactly is meant by the least moment of inertia?
You have calculated the least (minor axis) moment of inertia by assuming the 4 feet as your 'b' and 2 feet as your 'h'. The major axis moment of inertia is much greater ( using 2 feet as the 'b' and 4 feet as the 'h'); hence, the wall is much less stable along the weak axis, and thus, the least moment of inertia applies.

ok I see... so if the rectangle was rotated than the major axis would be calculated with the base being 2 and height being 4.

## 1. What is stability in relation to moment of inertia?

Stability refers to the ability of an object to maintain its equilibrium, or stay in a steady position. Moment of inertia is a measure of an object's resistance to changes in its rotational motion. Therefore, stability is directly related to the moment of inertia of an object.

## 2. How is moment of inertia calculated?

Moment of inertia is calculated by taking the sum of the masses of all the particles in an object multiplied by the square of their distance from the axis of rotation. This is represented by the equation I = Σmr², where I is the moment of inertia, m is the mass of the particle, and r is the distance from the axis of rotation.

## 3. What factors affect the moment of inertia of an object?

The moment of inertia of an object is affected by its mass, shape, and distribution of mass. Objects with a larger mass or a more spread out mass distribution will have a higher moment of inertia, making them more resistant to changes in rotational motion.

## 4. How does moment of inertia affect an object's stability?

The higher the moment of inertia of an object, the more stable it will be. This is because a higher moment of inertia means that more force is required to change the object's rotational motion, making it less likely to tip over or lose its balance.

## 5. Can the moment of inertia of an object be changed?

Yes, the moment of inertia of an object can be changed by altering its mass, shape, or distribution of mass. For example, adding weights to different parts of an object can change its moment of inertia and affect its stability. However, the total amount of mass and its distribution must remain constant for the moment of inertia to remain unchanged.