3. You have a quarter disc in the first quadrant (see figure below) with surface density ? = x + y. Find the center of mass coordinates x? and y?.
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** The region is a quarter circle in the first quadrant with radius 1. We can describe it in polar coordinates as: $$0 \le r \le 1, \quad 0 \le \theta \le \frac{\pi}{2}$$ The surface density is given by: $$\sigma = x + y$$ We need to convert this to polar Show more…
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