Consider a thin wire bent in the form of a circular arc. Polar coordinates are used to calculate the centroid of this quarter circular wire segment effectively. The centroid of the arc can be computed by dividing the wire into small differential elements, where each element has a length equal to the radius times the differential angle. The x and y-coordinates for the element's centroid can be expressed in terms of the radius and the angle made by the element with respect to the x-axis. The centroid of the arc is then calculated by computing the weighted average of all these elements. As the wire subtends a quarter circle, the expression can be integrated from the limits of zero to ℼ over two. The result yields the centroid coordinates for a quarter circular wire segment. The x and y-coordinates of the centroid are numerically equal due to the circular symmetry of the problem.