Decomposing the arc length of a circular arc segment

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  • Thread starter jumbo1985
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  • #1
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A particle travels along a circular arc segment centered at the origin of the Cartesian plane with radius R, a start angle θ1 and an end angle θ2 (with θ2 ≥ θ1 and Δθ = θ2 - θ2 ≤ 2π). The total distance traveled is equal to the arc length of the segment: L = R(Δθ).

I would like to find the distance covered by the particle along the X axis and the distance covered by the particle along the Y axis.

I'm not sure how to do this unless I break up the arc at each quadrant crossing and analyze the pieces separately.

Any tips are greatly appreciated.
 

Answers and Replies

  • #2
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Distance covered as in "if you go back and forth you count it twice"? You can write down an integral that works in general, but analyzing 2 special cases is easier.
 
  • #3
19
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Yes, exactly - If you go back and forth you count it twice. I'm looking for one elegant expression in terms of x and in terms of y but that may not be possible?
 
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