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Ratios of Bases and Circumferences

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ScissorsRunWithYou
 
Reply Fri 5 Nov, 2004 08:00 pm
So, you have a cup. The cup is part of a cone. The part of the cone with the point cut off. So, one base will obviously be smaller than the other. You have the bottom ( which will be the smaller one in this, we'll call it 'b' ) and the top (which, of course, will be larger. We'll call this "m"). We put this cup on its side ontop a flat surface and give it a little push and it will roll to form a circle. The cup will also rotate a number of times. My question is . . is the ratio of the size of the bottom to the size of the bottom play a factor in how many rotations the cup will make? If it does, can you please explain it to me?
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DrewDad
 
  1  
Reply Fri 5 Nov, 2004 09:48 pm
The angle of the vertex of the cone is what determines the number of rotations the cup will make. The ratio of the ends of your conic section are meaningless without the length of the section as well.
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ScissorsRunWithYou
 
  1  
Reply Fri 5 Nov, 2004 10:59 pm
MerlinsGodson wrote:
The angle of the vertex of the cone is what determines the number of rotations the cup will make. The ratio of the ends of your conic section are meaningless without the length of the section as well.


How do you find the angle of the vertex of the cone with just the bases of the cup?
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ScissorsRunWithYou
 
  1  
Reply Fri 5 Nov, 2004 11:21 pm
ScissorsRunWithYou wrote:


How do you find the angle of the vertex of the cone with just the bases of the cup?


Well, with just the parts of the cup.. The height, the slope of the side and the bases.
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DrewDad
 
  1  
Reply Fri 5 Nov, 2004 11:29 pm
Place the cup on the larger end. Now calculate the angle of the side of the conic section to vertical. Double that and you have the angle of the vertex.

Basically, it is a right-triangle problem. Put a plane through the diameter of the cup. This will give a tetrahedron.

Code:
___
/ \
/ \
/_______\


Now drop a vertical line from the top-right corner:

Code:
/|
/ |
/__|


Calculate the angle of the top of the triangle.
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ScissorsRunWithYou
 
  1  
Reply Fri 5 Nov, 2004 11:35 pm
Edit: Actually, I'm a little confused. When you draw a vertical line from the top right corner, you do not get a triangle. At least, not on the side your picture corresponds to. Am I missing something?
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DrewDad
 
  1  
Reply Sat 6 Nov, 2004 01:51 pm
Yes. You're missing the fact that I said right and meant left. LOL.
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