4) The mass of the homogeneous thin metal plate is 65.0 kg. a) b) c) Find the coordinates of the center of mass. Find the mass moment of inertia about the z-axis. Find the mass moment of inertia about the axis parallel to the z-axis, but going through the center of mass. Don't forget to include the units for everything. T 10.0m 'mm 5.00m 'L 5.00m . L 6.00m 2. Mass moment of inertia about the z-axis: - The moment of inertia about the z-axis can be calculated using the parallel axis theorem. - The moment of inertia of the rectangle about its centroid is: [Irectangle = 12 . mass (Length? + Width?) ] - The moment of inertia of the semicircle about its centroid is: Isemicircle = mass . (Xcenter of mass)-] - The total moment of inertia about the z-axis is the sum of these two: [Iz = Irectangle + Isemicircle] 3. Mass moment of inertia about an axis parallel to the z-axis but going through the center of mass: - The moment of inertia about this axis is: [parallel = 4 . mass . (Length + Width?) + mass . (Xcenter of mass)"]