Visualizing Rotations: Understanding 3D Models Bounded by Parabolas

In summary, the conversation is about creating a 3D model of a figure bounded by y=4 and y=x^2 that is rotated about the x-axis. The speaker initially thought it would form an hourglass shape, but the other person corrects them and explains that it would actually form a paraboloid of revolution. The conversation ends with the speaker asking for more help in understanding the concept.
  • #1
Codyt
27
0
Ok, I have to make a 3D model of a figure bounded by y=4 and y=x^2 that is rotated about the x-axis. I believe it will form an hour glass shape and I am putting two half spheres together to form the model, is this right?
 
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  • #2
Codyt said:
Ok, I have to make a 3D model of a figure bounded by y=4 and y=x^2 that is rotated about the x-axis. I believe it will form an hour glass shape and I am putting two half spheres together to form the model, is this right?

No!...

(edit... if you revolve around the Y AXIS, THEN) It's called a "Paraboloid of revolution". It looks like a "Dot" (the candy made by the tootsie roll company)
 
Last edited:
  • #3
Can you please explain this, I looked up what you said, but I still cannot see how that would be formed by my shape. The paraboloid of revolution looks more like what would be formed by rotating in about the y axis. Anyh help is appreciated.
 
  • #4
Codyt said:
Can you please explain this, I looked up what you said, but I still cannot see how that would be formed by my shape. The paraboloid of revolution looks more like what would be formed by rotating in about the y axis. Anyh help is appreciated.

You're right. I wasn't paying attention! I'll think about a good way to visualize this.
 

1. What does it mean to rotate around the x axis?

Rotating around the x axis means to rotate an object or point in a three-dimensional coordinate system around the horizontal x-axis. This causes the object to move in a circular motion in the x-z plane.

2. How do you calculate the coordinates of a point after rotating around the x axis?

To calculate the new coordinates of a point after rotating around the x axis, you can use a rotation matrix. The formula is:
x' = x
y' = y * cos(theta) - z * sin(theta)
z' = y * sin(theta) + z * cos(theta)
Where (x, y, z) are the original coordinates of the point, (x', y', z') are the new coordinates, and theta is the angle of rotation.

3. What is the difference between rotating around the x axis and the y axis?

The main difference between rotating around the x axis and the y axis is the direction of rotation. Rotating around the x axis causes the object to move in a circular motion in the x-z plane, while rotating around the y axis causes the object to move in a circular motion in the y-z plane.

4. Can you rotate around the x axis in two dimensions?

No, rotating around the x axis requires a three-dimensional coordinate system where the x axis is one of the three axes. In two dimensions, there is only the x and y axis, so rotating around the x axis is not possible.

5. What is the purpose of rotating around the x axis?

Rotating around the x axis is used in many fields, including mathematics, physics, and computer graphics. It can be used to transform an object or point in a three-dimensional space, create 3D animations, and solve geometric problems involving rotation.

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