Very basic statics question/moment of inertia

In summary, the formula hb^3 /12 can be used to compute the moment of inertia about the y-axis for a triangular shape in the 2nd quadrant, as long as one side is collinear with the y-axis. However, this formula is only applicable to right triangles and there are more general formulas available for more complex triangular shapes.
  • #1
encorelui2
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Statics: If computing the moment of inertia about the y-axis of a triangular shape in the 2nd quadrant(not touching the x-axis); would i still use hb^3 /12
 
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  • #2
encorelui2 said:
Statics: If computing the moment of inertia about the y-axis of a triangular shape in the 2nd quadrant(not touching the x-axis); would i still use hb^3 /12

Yes, you would, but be careful which sides you use for 'b' and 'h'. You haven't specified which is measured along the x-axis and which is measured along the y-axis. This formula only works for right triangles, incidentally.

http://en.wikipedia.org/wiki/List_of_area_moments_of_inertia
 
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  • #3
encorelui2: So far, your formula looks correct. And, it is not limited to right triangles.

It does not matter whether it touches the x-axis or not. And it does not matter what quadrant it is in. It only needs to have one side coincident (collinear) with the y axis, assuming b is the horizontal width of your triangle.
 
  • #4
nvn said:
encorelui2: So far, your formula looks correct. And, it is not limited to right triangles.

It does not matter whether it touches the x-axis or not. And it does not matter what quadrant it is in. It only needs to have one side coincident (collinear) with the y axis, assuming b is the horizontal width of your triangle.

I apologize for not posting more complete information, but the OP's formula for the moment of inertia of a triangle is indeed only applicable to right triangles. The following link gives formulas for the area properties for more general triangular shapes:

http://www.efunda.com/math/areas/triangle.cfm
 
  • #5


Yes, the formula for moment of inertia about the y-axis, given by Iy = hb^3/12, can still be used for a triangular shape in the 2nd quadrant that does not touch the x-axis. This is because the formula is based on the shape's geometry and does not depend on its position in the coordinate plane. As long as the shape remains triangular and its base and height are known, the formula can be used to calculate its moment of inertia about the y-axis.
 

1. What is the definition of moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by summing the products of each particle's mass and the square of its distance from the axis of rotation.

2. How is moment of inertia different from mass?

Moment of inertia is often compared to mass because they both involve the concept of inertia, but they are not the same thing. While mass is a measure of an object's resistance to changes in linear motion, moment of inertia is a measure of an object's resistance to changes in rotational motion.

3. What is the formula for calculating moment of inertia?

The formula for calculating moment of inertia depends on the shape and distribution of an object's mass. For a point mass, the formula is I = mr², where m is the mass and r is the distance from the axis of rotation. For more complex objects, the formula is I = ∫r² dm, where r is the distance from the axis of rotation and dm is the infinitesimal mass element.

4. How does moment of inertia affect an object's rotational motion?

Moment of inertia plays a significant role in an object's rotational motion. The greater the moment of inertia, the more force is required to change an object's rotational speed. This means that objects with a larger moment of inertia will rotate more slowly than objects with a smaller moment of inertia when the same amount of force is applied.

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

Moment of inertia is an important concept in many fields, including physics, engineering, and biomechanics. It is used in designing structures and machines that rotate, such as bridges, wind turbines, and car engines. It also plays a role in understanding the movement and stability of objects in sports, such as figure skating and diving.

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