Arc Length

  • Thread starter eXmag
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  • #1
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Homework Statement


f4mkut.jpg



Homework Equations


The arc length equation?


The Attempt at a Solution


I don't know where to begin.
 
Last edited:

Answers and Replies

  • #2
CompuChip
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What is "the arc length equation", do you mean [itex]L = r \theta[/itex] (with [itex]\theta[/itex] in radians)? If so, yes, that is useful. r is given, how do you find [itex]\theta[/itex]?

Also in your image you have drawn a vertical line stating r = 200. That line is not a radius of the circle, did you mean to put the label next to the line OB?
 
  • #3
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O (zero) is for origin and 200 is the radius, i just put the line there to indicate where the center of the circle is. The circle is not centered with the origin that is why, just shifted to the right.
 
  • #4
CWatters
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I would add two lines to the drawing...

1) From B to the center of the circle
2) From point B down to the x-axis.

Some triangles will be obvious.

I'd also mark the angle A-(center of circle)-B and call it θ

Then start with L = rθ and make substitutions. eg find a way to express θ in the required co-ordinates.
 
  • #5
CompuChip
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O (zero) is for origin and 200 is the radius, i just put the line there to indicate where the center of the circle is. The circle is not centered with the origin that is why, just shifted to the right.

I missed that, my bad.
Maybe it is slightly easier if you shift the center of the circle to the origin, which will make the coordinate of B (x - c, y) instead of (x, y), where (c, 0) is the center of the circle. Then, as I said, you will need to find [itex]\theta[/itex].
 
  • #6
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Thanks so much for your help guys, i found the answer :) Regarding the L=r theta, I actually found an easier way to calculate the arc length. If u divide the theta angle in degrees by 360 and put it equal to the L divided by the circumference it gives you the exact same answer. Like this, degree/360 = L/circumference and solve for L.
 

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