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Example: Find the moment of inertia of a uniform rectangular plate of mass 5 kg, width 2 m (along x) and height 3 m (along y), about an axis perpendicular to the plate through its centre. Step 1: Identify axes. - x‑axis lies along the width (2 m). - y‑axis lies along the height (3 m). - z‑axis is perpendicular to the plate. Step 2: Use the perpendicular axis theorem: I_z = I_x + I_y. Step 3: Find I_x and I_y. - For a thin rectangular plate, I_x = (1/12) M * (height)^2 = (1/12) * 5 kg * (3 m)^2 = (1/12) * 5 * 9 = 3.75 kg·m². - I_y = (1/12) M * (width)^2 = (1/12) * 5 kg * (2 m)^2 = (1/12) * 5 * 4 = 1.666... kg·m². Step 4: Add them: I_z = 3.75 + 1.666... = 5.416... kg·m². Answer: The moment of inertia about the perpendicular axis is approximately 5.42 kg·m².