8. of the Workbook we were asked to find the mass and centre of mass of the 1.5- semicircular lamina {x² + y² < 1, y 2 0} if the density equals the distance r from the origin. We found in class that the mass is 0.5- M = 1/3 and that the coordinates of the centre of mass are -1.5 -1 -0.5 0 0.5 1 1.5 i = 0 ỹ = 3/2n Take care with what these mean. For example, ỹ is the average value of the y-coordinates of all the points in the lamina, where this is a weighted average, each “point" weighted by its mass. Here's the problem: what is ĩ, the average value of r, over the same semi-circular lamina, and with the same density (egual to the distance r from the origin)?

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