Finding Second Moment of Inertia for Shaded Area Through Centroid?

In summary, the conversation discusses determining the second moment of inertia about the horizontal and vertical axes for a shaded area with respect to x and y axes through the centroid of the area. The solution involves using calculation axes shown in Fig. 6.7 and reading the text to accurately follow the process. It is not sufficient to assume that one picture applies in all cases.
  • #1
werson tan
183
1

Homework Statement


determine the second moment of inertia about the horizontal axis and vertical axis for the shaded area with respect to x and y axes through the centroid of the area .

Homework Equations

The Attempt at a Solution


Since the x and y axes is drawn thru centroid , why not the y for part 1 = 0mm ? y for part 2 = -30mm?
 

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  • #2
werson tan said:

Homework Statement


determine the second moment of inertia about the horizontal axis and vertical axis for the shaded area with respect to x and y axes through the centroid of the area .

Homework Equations

The Attempt at a Solution


Since the x and y axes is drawn thru centroid , why not the y for part 1 = 0mm ? y for part 2 = -30mm?
Because the axes being used for the calculation are not the same ones shown in Fig. 6.7. The calculation axes are shown at the lower right-hand part of the page, just above the table.

You must read the text in order to follow what is going on; you can look at one picture and assume it applies regardless.
 
  • #3
SteamKing said:
You must read the text in order to follow what is going on; you can look at one picture and assume it applies regardless.
You meant 'cannot', right?
 
  • #4
haruspex said:
You meant 'cannot', right?
Yes.
 

Related to Finding Second Moment of Inertia for Shaded Area Through Centroid?

1. What is the centroid of an object?

The centroid of an object is the geometric center of the object, also known as its center of mass. It is the point where all the weight of the object can be considered to be concentrated.

2. Can an axis pass through the centroid of an object?

Yes, an axis can pass through the centroid of an object. In fact, the centroid is often used as a reference point for determining the location of axes passing through an object.

3. How does an axis passing through the centroid affect an object's stability?

An axis passing through the centroid of an object does not affect its stability, as the centroid is the point of balance for the object. This means that the object will not rotate or tip over when a force is applied along this axis.

4. What is the significance of an axis passing through the centroid in engineering?

In engineering, an axis passing through the centroid is often used as a reference point for calculating moments of inertia, which is important for analyzing the structural stability and strength of an object.

5. How do you determine the location of an axis passing through the centroid of a complex object?

The location of an axis passing through the centroid of a complex object can be determined by finding the centroid of each individual component of the object and then finding the average location of all the centroids. This average point will be the centroid of the entire object and can be used as the reference point for the axis.

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