# HOMEWORK H32.B ## 35 thoughts on “HOMEWORK H32.B”

1. Rohit Ravi Harapanhalli says:

We just have to add up the individual contributions of both semicircles towards the y centroid and second area moment, right?

1. Kaushal Kamal Jain says:

Yes

2. Nasser Sadiq Alsinan says:

will the distance from the y-centroid of the shape to the bottom circle be the y-centroid of the bottom circle plus the y-centroid or minus the y-centroid since it's in the negative direction?

1. Sean Geno Cosejo Sales says:

I think it would be subtracting because adding would lead to a centroid higher on the y axis while subtracting would yield a centroid closer to y = 0, which should be the case.

1. Zongxin Yu says:

Sean's physical feeling is right, that adding a bottom semi-circle brings y-centroid closer to zero. However, Ashley and Bowen's approach is more rigorous, and it allows you staying with the formula safely. I would recommend you to think in this way.

2. Ashley Molnar says:

It would be a positive area, but a negative y-centroid, which would lead to subtracting in the centroid equation!

1. park1153 says:

This shows us the interesting comparison between the first previous problem. Both parts contributing negative y-centroids in different ways.

1. Corina Marie Capuano says:

Does this imply that the centroid for both of these areas is the same?

1. Jacob Pierce Harmon says:

No, because the total area of the shapes are different.

2. Ruth Ivania Guerra says:

Yes. Poisitive area for both and negative centroid for the smaller part of the circle. Then you weight the centroid with the areas and then solve for the whole figure (both semicircle) centroid, that end up being in the positive part of the plane since it has a larger area.

3. Bowen Zheng says:

I agree with previous reply. Both areas are positive, the centroid of larger semicircle is positive and that of the smaller semicircle should be negative. Like we add them together. Centroids of larger one + (-)centroids of smaller one

4. Mohnish Y Shah says:

You should be subtracting it since the other half is below the x axis. However, the areas should remain positive for you calculation.

3. Deepa Jayasankar says:

Is there a good way to estimate what the combined moment of this type of question should be?

1. Zach Mullen says:

I think your best bet to estimate that value would be to look at the tabulated values for the individual shapes. You know the second area moment has to be smaller than that of a full circle of radius R which is (pi*R^4)/4 but larger than that of a semicircle of radius R which is (pi*R^4)/8.

As long as your answer was in that range, you'd be close.

1. Zongxin Yu says:

Zach's approach is easy to understand. Or you can assume the radius of the the bottom circle is d. Then put d=R/2 at the last step you can get what is asked in the problem. You can check it by setting d=R, then the y-centroid of the combined shape would be zero, and the area, the second area moment for a full circle as Zach mentioned.

2. Rhutuja Jaideep Patil says:

You can take the individual moments about their own centroids and then use the parallel axis theorem to find the combined second moment of the shaded portion about the overall centroid.

4. Ammar Al Nas says:

I agree with ashley's method because if you want to find the contribution of areas on a composite areas centroid you use the displacement , the location to be exact ,not distance from a neutral point like the origin,for example , similar to H12 when negative positions were used.

5. Jessika Kathleen Wahlbin says:

How would you change your approach to solving the problem if the bending was in the y-direction instead of the z-direction?

1. Mohnish Y Shah says:

In that case you would be calculating the centroid in the z direction. Other than that, you follow a near identical process that you did for bending in the z direction.

6. Mohnish Y Shah says:

In that case you would be calculating the centroid in the z direction. Other than that, you follow a near identical process that you did for bending in the z direction.

7. Jennifer Leigh Smith says:

Just to make sure we use (A1Y1 + A2Y2)/(A1+A2) for this problem. Then for problem A we use (A1Y1 - A2Y2)/(A1-A2)?

1. tc says:

Yeah I subtracted for problem A and added for this problem

2. Jacob Pierce Harmon says:

As long as you remember that Y2 is negative in this problem, that works.

1. vwelker says:

Does knowing that y2 is negative end up affecting the end answer in the 2nd moment of inertia?

8. Hardy says:

When finding the combined second moment will each distance be different, based on each component's ycentroid from the combined one?

1. Ruth Ivania Guerra says:

I dound the second moment of inertia for each one and weight it, as when finding the ycentroid for each. I am not sure if this is correct. Can someone afirm if this is correct path to solve the problem?

2. Maggie Elyse Craig says:

There is only one centroid of the composite, so when finding the second moment, I think the distance is the separate part's distance from its individual centroid to the composite centroid, in this case in the y direction. At least that is my understanding.

9. Ruth Ivania Guerra says:

Can you do a table like the one we used to do in previous problems to find the centroids or is better just to follow equations and skip the table?

1. vwelker says:

I would recommend just following the equations. It's less confusing this way, only finding what you need.

2. Chirag Pradeep Nimani says:

It's much easier and faster when we just follow the equations. It took lesser amount of time doing it that way

10. James Sun says:

Is the total area the larger circle minus the small circle like Problem A or just add them together?

1. Sai says:

The total area would be the large semicircle and the small semicircle added together.

11. James Sun says:

Does z direction means z-axis?

12. Yubo Song says:

does y2 in this problem count as a negative contribution to intertia?

13. Cullen James Barber says:

Yes, you subtract it from the 2nd Area moment