Where did the dx go from the bottom portion of the equation? if dV = (pi)r^2 dx and you replace the dV on both the top and bottom, where did the dV go on the bottom?
It does appear to be "counter intuitive", but we are following the strict definition of the centroid and thus it is giving us the correct answer.. (In the y-direction th center of mass is at y = 0 because of the symmetry).
Call you help me figure something out? Okay, what I'm looking for is the center of mass (or "gravity") of a hollow sphere with a spherical cap removed from one side (that is less than a hemisphere in size). Kinda like one one those round wine glasses but without the flat base. Also, I want to confirm that I have the correct center of mass of the (hollow bowl-shaped) spherical cap. This video is the closest I've seen to what I am looking for. I'm trying to use this to prove Newton's shell theorem using an alternative method from triple integrals and so on... If you help me, I'll give you all the details of my new proof and you can go ahead and do a video on it if you want.
A semi circle will have the same center of mass as a half barrel, same shape at every cross section, but each cross section of a semi sphere is different.
Welcome to the channel! Because of the symmetry, the centroid in the Y-direction is on the x-axis. If the object is oriented up instead of sideways, work the problem exactly the same way, but exchange x for y.
+dipesh rathi It depends on the integration technique. There are several ways in which you can integrate to find the volume of an object. Because of the symmetry of the object we didn't have to integrate in the z-direction to find the answer.
explain so clear that I can understand using 1.5x speed, thx!
Glad it is helping.
This helped me a lot.May GOD bless u sir
We are glad these videos are helpful, and yes God has blessed us. May He bless you and your family as well.
Where did the dx go from the bottom portion of the equation? if dV = (pi)r^2 dx and you replace the dV on both the top and bottom, where did the dV go on the bottom?
We replaced the integral in the denominator with the actual volume (since that is what the integral would have given us anyway).
Sir please make camera in side when you write on board because by live writing demonstration it will easy to learn.
since the strip we are cutting is vertical shouldnt it be Ydv?????
It does appear to be "counter intuitive", but we are following the strict definition of the centroid and thus it is giving us the correct answer.. (In the y-direction th center of mass is at y = 0 because of the symmetry).
Call you help me figure something out?
Okay, what I'm looking for is the center of mass (or "gravity") of a hollow sphere with a spherical cap removed from one side (that is less than a hemisphere in size). Kinda like one one those round wine glasses but without the flat base.
Also, I want to confirm that I have the correct center of mass of the (hollow bowl-shaped) spherical cap.
This video is the closest I've seen to what I am looking for.
I'm trying to use this to prove Newton's shell theorem using an alternative method from triple integrals and so on...
If you help me, I'll give you all the details of my new proof and you can go ahead and do a video on it if you want.
This helped me thanks a lot for the video sir!
When we integrate the denominator dV the answer is something else. Can you explain why?
The answer should be exactly the same.
why we're are not taking the z axis and what is the basic way to find center of continuous body I think I must watch that first
by basic way I mean the actual logic to find the center of mass of all bodies if I understand that I will easily understand this video
Because of the symmetry, the center of mass in the z-direction is on the axis.
Sir could you explain why the center of mass of a semi circle is 4r/3pi while a semi sphere 3r/8? I can't visualize the difference. Thank you. :)
Is it because the semi circle "with uniform density" looks like a half moon cake?
A semi circle will have the same center of mass as a half barrel, same shape at every cross section, but each cross section of a semi sphere is different.
Explained very well
Thank you!
hello from Egypt :) I have a question ... what about if it on the y direction ? i wanna send a photo to show you ^_^ i cannot solve it
Welcome to the channel! Because of the symmetry, the centroid in the Y-direction is on the x-axis. If the object is oriented up instead of sideways, work the problem exactly the same way, but exchange x for y.
i want a video for hollow semi sphere
It is applicable for segment which is smaller than semisphere?????? Pls reply
yes. The limits of integration will be different
Why integral dV in the denominator is (2/3)Pi R^3.
The volume of a sphere = (4/3) pi R^3, so the volume of a half sphere is (1/2) (4/3) pi R^3
why we donot write value of the dv in the numenator same as in the denomenator instead of it we write 2/3*pie^3
Why cant we use angle approximation ??
Did you try it?
Michel van Biezen yes i did but i get the wrong answer...R/2
That is why I recommend you use the technique shown in the video.
But where we wrong in angle approximation
What is he saying at the beginning of every vid?
"Welcome to Ilectureonline"
and im sitting here thinking he's been saying "welcome to electro-online" for the past year
thanks sir
Most welcome 🙂
sir why we didn't include z since it is 3d object
+dipesh rathi It depends on the integration technique. There are several ways in which you can integrate to find the volume of an object. Because of the symmetry of the object we didn't have to integrate in the z-direction to find the answer.
Integrate 1 = x?? Why did you write integrate dv = 2/3pie R3??
But the answer is 2/3pieR3X where is the X sir please explain.. 🖤 🙏
The integral in the denominator is equal to the volume of the semi-sphere. (1/2) (4/3) (pi) (R^3)
thanks a loot🙏
You are welcome. Glad you found our videos. 🙂
Michel Van Biezen for president!!!!!!
Thank you so much
👍
tysssssm
You are very welcome. 🙂
please be safe in coranvirus times sir. my prayers are with you