# Moment of Inertia for Square Plate on X Axis

• fightnchikn
In summary, to find the moment of inertia for a square uniform plate with length h on the sides, you can use the formula x^2dm and integrate it over the area of the plate. The y integral is simple and the remaining integral is from -h/2 to +h/2, or twice the integral from 0 to h/2 due to symmetry.
fightnchikn
helllo, I am having trouble finding the moment of inertia for a square uniform plate with length h on the sides...how do you go about it when the interia is about the x axis...the z axis is perpendicular to the square in this case... i understand how to do it when it is with respect to the z axis...the double intergral and all but when its on the xaxis i get confused...how do you set that up.

Last edited:
fightnchikn said:
helllo, I am having trouble finding the moment of inertia for a square uniform plate with length h on the sides...how do you go about it when the interia is about the x axis...the z axis is perpendicular to the square in this case... i understand how to do it when it is with respect to the z axis...the double intergral and all but when its on the xaxis i get confused...how do you set that up.
It should be easier to do it for the x-axis than for the z axis. I assume the origin is in the center of the plate, with the x-axis being a line that divides the plate into two equal rectangles. Consider a mass element dm = σdxdy and integrate x^2dm over the area of the plate. The y integral is very simple since there is no function of y in the integrand. You just get h, which is constant for all x. All that is left is the integral of x^2.

Now when I integrate what do I integrate from 0 to h?

fightnchikn said:
Now when I integrate what do I integrate from 0 to h?
If the axis is as I assumed, it is from -h/2 to +h/2. By symmetry, you could do twice the integral from 0 to h/2 and get the same result.

## 1. What is moment of inertia for a square plate on the X axis?

The moment of inertia for a square plate on the X axis is a measure of its resistance to rotation around the axis. It is represented by the symbol I and has units of mass times squared distance.

## 2. How is moment of inertia calculated for a square plate on the X axis?

The moment of inertia for a square plate on the X axis can be calculated using the equation I = (1/12) * M * L^2, where M is the mass of the plate and L is the length of one side of the square.

## 3. What factors affect the moment of inertia for a square plate on the X axis?

The moment of inertia for a square plate on the X axis is affected by its mass, shape, and distance from the axis of rotation. A larger mass or longer length will result in a higher moment of inertia, while a thinner plate or closer distance to the axis will result in a lower moment of inertia.

## 4. How does the moment of inertia for a square plate on the X axis relate to its rotational kinetic energy?

The moment of inertia for a square plate on the X axis is directly proportional to its rotational kinetic energy. This means that a higher moment of inertia will result in a higher rotational kinetic energy, and vice versa.

## 5. Can the moment of inertia for a square plate on the X axis be changed?

Yes, the moment of inertia for a square plate on the X axis can be changed by altering its mass, shape, or distance from the axis of rotation. For example, increasing the mass or length of the plate will increase its moment of inertia, while changing its shape or moving it closer to the axis will decrease it.

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