Why Is My Calculation of the Center of Mass for a Uniform Wire Incorrect?

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SUMMARY

The calculation of the center of mass for a uniform wire subtending an arc of 22 degrees with a radius of 1 meter involves converting the angle from degrees to radians. The correct formula for the x-coordinate of the center of mass is x = (2r/theta) * sin(theta/2), where theta must be in radians. The user initially calculated the center of mass as 0.01735 m but failed to convert the angle, leading to an incorrect result. After recognizing this error, the user corrected their approach.

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  • Knowledge of angular measurements in both degrees and radians
  • Basic physics concepts related to density and mass distribution
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Homework Statement


Find x coordinant of the the center of mass point of a uniform wire that subtends an arc of 22 degrees if the radius of the circular arc is 1m.


Homework Equations


I begin with: length = r*theta

Therefore M = density*r*theta

dm = density*ds = denisty*r8*d(alpha)

x= (1/M)*[integral of r*cos(alpha)*denisty*r*d(alpha) from (theta/2) to -(theta/2)

Thus, I get
x = (2r/theta)*sin(theta/2)



The Attempt at a Solution


I keep getting an answer of 0.01735 m. However, the online homework is telling me that it is not the correct answer.

I am not sure where in the above calculations I would have messed up. Could someone please point out where I have made an error?

Thank you in advance.
 
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okay nevermind I was forgetting to convert theta to radians.
 

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