Consider a plane homogeneous plate of density p bounded by the logarithmic spiral r = ke aθ and the radii θ = 0 and θ = π. Obtain the inertia tensor for the origin at r = 0 if the plate lies in the x1-x2 plane. Perform a rotation of the coordinate axes to obtain the principal moments of inertia, and use the results of the previous problem to show that they are

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IK = pk*P(Q - R), = pk P(Q+ R), ; = K+ 1; where 1 + 4a? etma R = V1 + 4a? 16(1 + 4a?)' Q = 2a