Let S be the lamina of mass density = 1 obtained by removing a circle of radius r from
Chapter 8, Problem 40(choose chapter or problem)
Let S be the lamina of mass density = 1 obtained by removing a circle of radius r from the circle of radius 2r shown in Figure 25. Let MS x and MS y denote the moments of S. Similarly, let Mbig y and Msmall y be the y-moments of the larger and smaller circles. (a) Use the Symmetry Principle to show that MS x = 0. (b) Show that MS y = Mbig y Msmall y using the additivity of moments. (c) Find Mbig y and Msmall y using the fact that the COM of a circle is its center. Then compute MS y using (b). (d) Determine the COM of S
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