Consider a wire of uniform density and mass M shaped into a quarter circle of radius R. The wire is located in the xy plane, with the origin at the focus of the quarter circle (i. e at the center of the circle of which the wire is part). Choose the x axis parallel to the line that connects the endpoints of the wire, so that the y-z plane is a plane of reflection symmetry for the wire. This means that the ends of the wire are located at R/sqrt(2)*(1,1,0) and R/sqrt(2)*(-1,1,0) and that the wire can be described by the equation x^2 + y^2 = R^2. Required:
a. Calculate the moment of inertia tensor for rotation about the origin. Also calculate the location of the center of mass for the wire.
b. Using the results from (a) and the generalized parallel axis theorem, find the moment of inertia tensor for rotation about one of the wire ends, with the x-axis along the line connecting the two ends of the wire.