Moment of Inertia about y axis composite body

In summary, the moment of inertia (in4) about the y-axis can be calculated using the formula Iy = 0.25πr^4 for a circle and Iy = (1/12)hb^3 for a triangle. The parallel axis theorem states that Iy = Iy' + A[d(x)]^2. Therefore, the moment of inertia is a combination of the two shapes and the correct answer is most likely (a) 39,500.
  • #1
engstrom2278
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Homework Statement



The moment of inertia (in4) about the y-axis is most nearly
(a) 39,500 (b) 37,600 (c) 38,700 (d) 36,400

Homework Equations



Iy(circle)= .25(pi)(r^4)
Iy(triangle)= (1/12)h(b^3)
parralel axis theorem= Iy=Iy'+A[d(x)]^2


The Attempt at a Solution



Iy(circle)= 39760
I don't know what to do with the subtraction of the triangles. Will they cancell each other out and the answer would be nearest (a)?
 

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  • #2
welcome to pf!

hi engstrom2278! welcome to pf! :wink:
engstrom2278 said:
… I don't know what to do with the subtraction of the triangles. Will they cancell each other out and the answer would be nearest (a)?

are the triangles holes?

then treat them as having negative mass :smile:

(and no, they don't cancel each other, they combine)
 

FAQ: Moment of Inertia about y axis composite body

1. What is the moment of inertia about the y-axis for a composite body?

The moment of inertia about the y-axis for a composite body is a measure of the body's resistance to rotational motion about that axis. It is calculated by summing the individual moments of inertia of all the constituent parts of the body.

2. How is the moment of inertia about the y-axis affected by the shape of the composite body?

The moment of inertia about the y-axis is affected by both the mass and distribution of mass around the y-axis of each individual component of the composite body. The more mass is located farther from the axis of rotation, the higher the moment of inertia will be.

3. Can the moment of inertia about the y-axis be negative?

No, the moment of inertia about the y-axis cannot be negative. It is always a positive value as it represents the resistance to rotation.

4. What is the difference between the moment of inertia about the y-axis and the moment of inertia about the x-axis?

The moment of inertia about the y-axis and the moment of inertia about the x-axis represent the body's resistance to rotation about two different perpendicular axes. The moment of inertia about the y-axis is affected by the mass and distribution of mass around the y-axis, while the moment of inertia about the x-axis is affected by the mass and distribution of mass around the x-axis.

5. How can the moment of inertia about the y-axis be used in real-world applications?

The moment of inertia about the y-axis is an important concept in physics and engineering, and it has many real-world applications. It is used in the design of structures, vehicles, and machinery to ensure stability and proper functioning. It is also used in sports and athletics to analyze the performance of athletes and their equipment.

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