Finding the Centroid of a Half-Cone: Tips and Troubleshooting

In summary, the conversation is about finding the centroid of a half-cone using cylindrical coordinates. The limits of integration used are 0 < r < 1, -pi/2 < theta < pi/2, and 0 < z < 1, and the mass is calculated using a triple integral. The individual's results do not match up with those in the book and they are seeking advice or assistance with their approach.
  • #1
wakko101
68
0
The question is this: find the centroid of the half-cone
sqrt(x^2 + y^2) <(oet) z <(oet) 1
and x >(oet) 0
(oet being or equal to, I apologize for the lack of sophistocated symbols). I thought I was doing it correctly, but my answers do not match up with those in the book.

I assumed that it would be wise to use cylindrical coordinates which would make r <(oet) 1 and z <(oet) 1. Now, for the limits of integration, I used

0 < r < 1,
-pi/2 < theta < pi/2 and
0 < z < 1.

The mass is the triple integral of [r dr dtheta dz]. And to find the centroid coordinates I take the triple integral of my particular coordinate multiplied by r and over the mass. I'm pretty sure I know how to integrate, so I assume that my mistake was in my limits or perhaps my choice of coordinate system.

Advice please and thank you...

Cheers,
Wakko. =)
 
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  • #2
It doesn't sound like you are doing anything obviously wrong. Maybe you could post your result and let people check it.
 

What is the centroid of a half cone?

The centroid of a half cone is the point where all the mass of the half cone can be considered to be concentrated. It is the center of gravity of the half cone.

How is the centroid of a half cone calculated?

The centroid of a half cone is calculated by taking the average of the centroids of all the infinitesimally thin slices that make up the half cone.

What is the significance of finding the centroid of a half cone?

Finding the centroid of a half cone is important in determining the stability and balance of the object. It also helps in calculating the moment of inertia of the half cone.

Can the centroid of a half cone be located outside the object?

No, the centroid of a half cone will always be located within the object. This is because the centroid is the point where the object is in perfect balance.

How does the centroid of a half cone differ from the centroid of a full cone?

The centroid of a half cone is located at a height that is one-third of the height of the full cone. This is because a half cone has half the volume of a full cone.

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