Moment of Inertia - Find Area Around Y-Axis

In summary, the problem is asking for the moment of inertia of an area about the y axis. The curve is represented by y2=2x and the shaded region is above the curve. The parallel axis theorem may be needed. The solution involves setting up the integral Iy= ∫x2ydx and substituting (2-/sqrt(2x)) for y. The correct answer is .762m^4.
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This is my first time posting in this site so if I left out any information or the information needs to be formatted differently I apologize ahead of time.

Homework Statement



Determine the moment of inertia of the area about the y axis.

The curve is represented by y2=2x, and the shaded region is the smaller area above the curve.

0m<x<2m
0m<y<2m

Homework Equations



Is the parallel axis theorem needed? If it is, why is the reason?

The Attempt at a Solution



Since the problem asks for moment of Intertia about the y-axis

1. Iy= ∫x2dA.

2. I chose my dA to be xdy because I need to find a "bar" perpendicular to the axis I am trying to find the moment of inertia about.

3. Solved

Iy= ∫x2ydx.
I substituded (2-/sqrt(2x)) for y and solved for the integral from (0<x<2)

My answer I got was 2.13m4 and the answer is incorrect.

Is my process correct or do I need to find different limits of integration?
 
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  • #2
I don't know how to close a thread, I found out my error was in the integration process.

Solved, Iy= .762m^4.
 

FAQ: Moment of Inertia - Find Area Around Y-Axis

What is moment of inertia and why is it important?

Moment of inertia is a measure of an object's resistance to rotational motion around an axis. It is important because it helps determine an object's stability, strength, and ability to resist bending or twisting forces.

How is moment of inertia calculated?

The moment of inertia around the y-axis can be calculated by using the formula I = ∫y2dA, where y is the distance from the y-axis to the infinitesimal element of area dA. This integral is typically solved using calculus.

What is the difference between moment of inertia around the x-axis and y-axis?

The moment of inertia around the x-axis is a measure of an object's resistance to rotational motion in the x-direction, while the moment of inertia around the y-axis is a measure of an object's resistance to rotational motion in the y-direction.

How does the distribution of mass affect moment of inertia?

The distribution of mass affects the moment of inertia by determining how far the mass is from the axis of rotation. The farther the mass is from the axis, the larger the moment of inertia will be.

What are some real-world applications of moment of inertia?

Moment of inertia is used in various engineering and physics applications, such as calculating the stability of structures, designing rotating machinery, and analyzing the motion of objects in space. It is also important in sports, such as figure skating and gymnastics, where the distribution of mass plays a role in an athlete's ability to perform certain movements.

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