Show that the center of mass of a semicircular wire of radius R is located at...

 

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Show that the center of mass of a semicircular wire of radius R is located at y =2R/ = (HINT: From the symmetry of the wire, it can be seen that the center of mass is located on the Y-axis. Calculate the y coordinate of the center of mass by converting the mass integral to an integral along the circumference and then convert it into an integral over theta) Show that the center of mass of a semicircular wire of radius R is located at y =2R/ = (HINT: From the symmetry of the wire, it can be seen that the center of mass is located on the Y-axis. Calculate the y coordinate of the center of mass by converting the mass integral to an integral along the circumference and then convert it into an integral over theta)