Question

What are the differences between centroid of shell, strips and discs in integral calculus?

Answer 1

@ganeshie8

Answer 2

I am well aware with the formulas but I don't know what type of centroid are meant by each one

Answer 3

@ParthKohli

Answer 4

What do you mean? Something like the center of mass?

Answer 5

Yeah Kinda. Centre of the shell generated, disc generated or strip generated when a specific portion is revolved around a specified axis

Answer 6

I don't understand your definition, but sounds like the center of mass to me.

Answer 7

Yeah I know they are the centre of the mass, but what is the difference between shell, strip and disc?

Answer 8

Hmm, I'm pretty sure you know what each of those look like

Answer 9

Nope I dont...

Answer 10

a shell is a hollow sphere
a disc is a flat plane circle (it's the boundary + the inside of a circle filled)
a strip could be rectangular or kinda like a sector, but the important part is that one dimension is wayyy thinner than the other

Answer 11

shell is the boundary of the shape generated by revolving 360 degrees the curve on an axis
disc is the the shape generated by revolving 360 degrees the curve on an axis
A strip is a shape generated by revolving a portion of the curve 360 degrees
Right?
Now my question is what is the difference between the centroid of shell and disc arent they supposed to be the same?

Answer 12

does the centroid have to lie on the thingy?

Answer 13

thingy is a reference to?

Answer 14

no, right? they're both centers of the respective figures, right?

Answer 15

Look if I have a function f(x). Now I revolve it 360 around an axis. Now no matter if I kept the inside hollow or filled, the centre wont change. Which means the centroid of shell and disc is same

Answer 16

yeah sure you can think of it that way

Answer 17

they're just geometrical centers of the respective figures. idk what's "same" about them

Answer 18

Coordinates of the centroid of a shell of function = coordinates of the centroid of a disc of a function right then?

Answer 19

That'd make all centroids the same in that case

Answer 20

So you agree by my previous assertation right?

Answer 21

That Coordinates of the centroid of a shell of function = coordinates of the centroid of a disc of a function right then?

Answer 22

@ParthKohli

Answer 23

Can you draw a picture of a specific example of what you're talking about?

Answer 24

I am talking about the centre of the shape generated when a curve is revolved 360 degrees around an axis. If the shape is hollow or filled, the centre of mass wont change right?

Answer 25

I think another way to look at what you're saying in 2D is that both shapes shown below will have the same coordinates for center of mass :