More practice questions

4. Q4. A uniform rectangular plate of mass 2 kg has sides 0.3 m and 0.4 m. Find its moment of inertia about the axis through its centre perpendicular to the plate.

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   I_z = M(a^² + b^²)/12 = 2 × (0.09 + 0.16)/12 = 0.5/12, about 0.0417 kg m^².

5. Q5. Three identical thin rods, each of mass m and length l, form an equilateral triangle. Find the moment of inertia of the frame about an axis through one corner, perpendicular to its plane.

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   The two rods that meet at the corner each rotate about an end: ml^²/3 each. The third rod’s centre is at the height of the triangle, (√3/2)l, from the corner, so by the parallel axes theorem its moment of inertia is ml^²/12 + m(3l^²/4) = 5ml^²/6. In total, 2(ml^²/3) + 5ml^²/6 = 3ml^²/2.

6. Q6. A body’s moments of inertia about two parallel axes, 0.2 m and 0.4 m from its centre of mass, differ by 0.12 kg m^². Find its mass.

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   I₂ − I₁ = M(0.4^² − 0.2^²) = M × 0.12, so M = 0.12/0.12 = 1 kg. The unknown I_cm cancels.