A 1.5kg point mass is fastened to a lightweight platform at the coordinate (0.40m,0.30m) in the xy-plane. Two distinct vertical axes are considered:
• Axis A: passes through the origin and is perpendicular to the plane.
• Axis B: passes through the point (0.20m,−0.10m) and is also perpendicular to the plane.
Complete the tasks below, showing all algebraic steps.
(a) Calculate the moment of inertia of the mass about Axis A.
(b) Calculate the moment of inertia of the mass about Axis B.
(c) Using your numerical results, derive a general algebraic expression for the difference between the moments of inertia about two parallel axes that are separated by a distance d. Verify that your derived expression is consistent with the values obtained in parts (a) and (b).